x^+2xy=60; x-y=4

$$x_{1} = - \frac{\sqrt{2} \sqrt{- 2 \sqrt[3]{50} + 2 \sqrt[3]{-3 + \sqrt{29}} + \sqrt[3]{20} \left(-3 + \sqrt{29}\right)^{\frac{2}{3}}}}{2 \sqrt[6]{-3 + \sqrt{29}}} + 1 + \frac{\sqrt{- 8 \sqrt{2} \sqrt{-3 + \sqrt{29}} - 2 \sqrt[3]{20} \left(-3 + \sqrt{29}\right)^{\frac{2}{3}} \sqrt{- 2 \sqrt[3]{50} + 2 \sqrt[3]{-3 + \sqrt{29}} + \sqrt[3]{20} \left(-3 + \sqrt{29}\right)^{\frac{2}{3}}} + 8 \sqrt[3]{-3 + \sqrt{29}} \sqrt{- 2 \sqrt[3]{50} + 2 \sqrt[3]{-3 + \sqrt{29}} + \sqrt[3]{20} \left(-3 + \sqrt{29}\right)^{\frac{2}{3}}} + 4 \sqrt[3]{50} \sqrt{- 2 \sqrt[3]{50} + 2 \sqrt[3]{-3 + \sqrt{29}} + \sqrt[3]{20} \left(-3 + \sqrt{29}\right)^{\frac{2}{3}}}}}{2 \sqrt[6]{-3 + \sqrt{29}} \sqrt[4]{- 2 \sqrt[3]{50} + 2 \sqrt[3]{-3 + \sqrt{29}} + \sqrt[3]{20} \left(-3 + \sqrt{29}\right)^{\frac{2}{3}}}}$$
=
$$- \frac{\sqrt{2} \sqrt{- 2 \sqrt[3]{50} + 2 \sqrt[3]{-3 + \sqrt{29}} + \sqrt[3]{20} \left(-3 + \sqrt{29}\right)^{\frac{2}{3}}}}{2 \sqrt[6]{-3 + \sqrt{29}}} + 1 + \frac{\sqrt{- 8 \sqrt{2} \sqrt{-3 + \sqrt{29}} - 2 \sqrt[3]{20} \left(-3 + \sqrt{29}\right)^{\frac{2}{3}} \sqrt{- 2 \sqrt[3]{50} + 2 \sqrt[3]{-3 + \sqrt{29}} + \sqrt[3]{20} \left(-3 + \sqrt{29}\right)^{\frac{2}{3}}} + 8 \sqrt[3]{-3 + \sqrt{29}} \sqrt{- 2 \sqrt[3]{50} + 2 \sqrt[3]{-3 + \sqrt{29}} + \sqrt[3]{20} \left(-3 + \sqrt{29}\right)^{\frac{2}{3}}} + 4 \sqrt[3]{50} \sqrt{- 2 \sqrt[3]{50} + 2 \sqrt[3]{-3 + \sqrt{29}} + \sqrt[3]{20} \left(-3 + \sqrt{29}\right)^{\frac{2}{3}}}}}{2 \sqrt[6]{-3 + \sqrt{29}} \sqrt[4]{- 2 \sqrt[3]{50} + 2 \sqrt[3]{-3 + \sqrt{29}} + \sqrt[3]{20} \left(-3 + \sqrt{29}\right)^{\frac{2}{3}}}}$$
=

0.763209519288102 + 2.34570995986582*i

$$y_{1} = -3 - \frac{\sqrt{- \frac{40}{\sqrt[3]{-60 + 20 \sqrt{29}}} + 4 + 2 \sqrt[3]{-60 + 20 \sqrt{29}}}}{2} + \frac{\sqrt{- \frac{16}{\sqrt{- \frac{40}{\sqrt[3]{-60 + 20 \sqrt{29}}} + 4 + 2 \sqrt[3]{-60 + 20 \sqrt{29}}}} - 2 \sqrt[3]{-60 + 20 \sqrt{29}} + 8 + \frac{40}{\sqrt[3]{-60 + 20 \sqrt{29}}}}}{2}$$
=
$$-3 - \frac{\sqrt{- \frac{40}{\sqrt[3]{-60 + 20 \sqrt{29}}} + 4 + 2 \sqrt[3]{-60 + 20 \sqrt{29}}}}{2} + \frac{\sqrt{- \frac{16}{\sqrt{- \frac{40}{\sqrt[3]{-60 + 20 \sqrt{29}}} + 4 + 2 \sqrt[3]{-60 + 20 \sqrt{29}}}} - 2 \sqrt[3]{-60 + 20 \sqrt{29}} + 8 + \frac{40}{\sqrt[3]{-60 + 20 \sqrt{29}}}}}{2}$$
=

-3.2367904807119 + 2.34570995986582*i

$$x_{2} = - \frac{\sqrt{2} \sqrt{- 2 \sqrt[3]{50} + 2 \sqrt[3]{-3 + \sqrt{29}} + \sqrt[3]{20} \left(-3 + \sqrt{29}\right)^{\frac{2}{3}}}}{2 \sqrt[6]{-3 + \sqrt{29}}} + 1 - \frac{i \sqrt{- 4 \sqrt[3]{50} \sqrt{- 2 \sqrt[3]{50} + 2 \sqrt[3]{-3 + \sqrt{29}} + \sqrt[3]{20} \left(-3 + \sqrt{29}\right)^{\frac{2}{3}}} - 8 \sqrt[3]{-3 + \sqrt{29}} \sqrt{- 2 \sqrt[3]{50} + 2 \sqrt[3]{-3 + \sqrt{29}} + \sqrt[3]{20} \left(-3 + \sqrt{29}\right)^{\frac{2}{3}}} + 2 \sqrt[3]{20} \left(-3 + \sqrt{29}\right)^{\frac{2}{3}} \sqrt{- 2 \sqrt[3]{50} + 2 \sqrt[3]{-3 + \sqrt{29}} + \sqrt[3]{20} \left(-3 + \sqrt{29}\right)^{\frac{2}{3}}} + 8 \sqrt{2} \sqrt{-3 + \sqrt{29}}}}{2 \sqrt[6]{-3 + \sqrt{29}} \sqrt[4]{- 2 \sqrt[3]{50} + 2 \sqrt[3]{-3 + \sqrt{29}} + \sqrt[3]{20} \left(-3 + \sqrt{29}\right)^{\frac{2}{3}}}}$$
=
$$- \frac{\sqrt{2} \sqrt{- 2 \sqrt[3]{50} + 2 \sqrt[3]{-3 + \sqrt{29}} + \sqrt[3]{20} \left(-3 + \sqrt{29}\right)^{\frac{2}{3}}}}{2 \sqrt[6]{-3 + \sqrt{29}}} + 1 - \frac{i \sqrt{- 4 \sqrt[3]{50} \sqrt{- 2 \sqrt[3]{50} + 2 \sqrt[3]{-3 + \sqrt{29}} + \sqrt[3]{20} \left(-3 + \sqrt{29}\right)^{\frac{2}{3}}} - 8 \sqrt[3]{-3 + \sqrt{29}} \sqrt{- 2 \sqrt[3]{50} + 2 \sqrt[3]{-3 + \sqrt{29}} + \sqrt[3]{20} \left(-3 + \sqrt{29}\right)^{\frac{2}{3}}} + 2 \sqrt[3]{20} \left(-3 + \sqrt{29}\right)^{\frac{2}{3}} \sqrt{- 2 \sqrt[3]{50} + 2 \sqrt[3]{-3 + \sqrt{29}} + \sqrt[3]{20} \left(-3 + \sqrt{29}\right)^{\frac{2}{3}}} + 8 \sqrt{2} \sqrt{-3 + \sqrt{29}}}}{2 \sqrt[6]{-3 + \sqrt{29}} \sqrt[4]{- 2 \sqrt[3]{50} + 2 \sqrt[3]{-3 + \sqrt{29}} + \sqrt[3]{20} \left(-3 + \sqrt{29}\right)^{\frac{2}{3}}}}$$
=

0.763209519288102 - 2.34570995986582*i

$$y_{2} = -3 - \frac{\sqrt{- \frac{40}{\sqrt[3]{-60 + 20 \sqrt{29}}} + 4 + 2 \sqrt[3]{-60 + 20 \sqrt{29}}}}{2} - \frac{\sqrt{- \frac{16}{\sqrt{- \frac{40}{\sqrt[3]{-60 + 20 \sqrt{29}}} + 4 + 2 \sqrt[3]{-60 + 20 \sqrt{29}}}} - 2 \sqrt[3]{-60 + 20 \sqrt{29}} + 8 + \frac{40}{\sqrt[3]{-60 + 20 \sqrt{29}}}}}{2}$$
=
$$-3 - \frac{\sqrt{- \frac{40}{\sqrt[3]{-60 + 20 \sqrt{29}}} + 4 + 2 \sqrt[3]{-60 + 20 \sqrt{29}}}}{2} - \frac{\sqrt{- \frac{16}{\sqrt{- \frac{40}{\sqrt[3]{-60 + 20 \sqrt{29}}} + 4 + 2 \sqrt[3]{-60 + 20 \sqrt{29}}}} - 2 \sqrt[3]{-60 + 20 \sqrt{29}} + 8 + \frac{40}{\sqrt[3]{-60 + 20 \sqrt{29}}}}}{2}$$
=

-3.2367904807119 - 2.34570995986582*i

$$x_{3} = \frac{\sqrt{2} \sqrt{- 2 \sqrt[3]{50} + 2 \sqrt[3]{-3 + \sqrt{29}} + \sqrt[3]{20} \left(-3 + \sqrt{29}\right)^{\frac{2}{3}}}}{2 \sqrt[6]{-3 + \sqrt{29}}} + 1 + \frac{\sqrt{- 2 \sqrt[3]{20} \left(-3 + \sqrt{29}\right)^{\frac{2}{3}} \sqrt{- 2 \sqrt[3]{50} + 2 \sqrt[3]{-3 + \sqrt{29}} + \sqrt[3]{20} \left(-3 + \sqrt{29}\right)^{\frac{2}{3}}} + 8 \sqrt[3]{-3 + \sqrt{29}} \sqrt{- 2 \sqrt[3]{50} + 2 \sqrt[3]{-3 + \sqrt{29}} + \sqrt[3]{20} \left(-3 + \sqrt{29}\right)^{\frac{2}{3}}} + 4 \sqrt[3]{50} \sqrt{- 2 \sqrt[3]{50} + 2 \sqrt[3]{-3 + \sqrt{29}} + \sqrt[3]{20} \left(-3 + \sqrt{29}\right)^{\frac{2}{3}}} + 8 \sqrt{2} \sqrt{-3 + \sqrt{29}}}}{2 \sqrt[6]{-3 + \sqrt{29}} \sqrt[4]{- 2 \sqrt[3]{50} + 2 \sqrt[3]{-3 + \sqrt{29}} + \sqrt[3]{20} \left(-3 + \sqrt{29}\right)^{\frac{2}{3}}}}$$
=
$$\frac{\sqrt{2} \sqrt{- 2 \sqrt[3]{50} + 2 \sqrt[3]{-3 + \sqrt{29}} + \sqrt[3]{20} \left(-3 + \sqrt{29}\right)^{\frac{2}{3}}}}{2 \sqrt[6]{-3 + \sqrt{29}}} + 1 + \frac{\sqrt{- 2 \sqrt[3]{20} \left(-3 + \sqrt{29}\right)^{\frac{2}{3}} \sqrt{- 2 \sqrt[3]{50} + 2 \sqrt[3]{-3 + \sqrt{29}} + \sqrt[3]{20} \left(-3 + \sqrt{29}\right)^{\frac{2}{3}}} + 8 \sqrt[3]{-3 + \sqrt{29}} \sqrt{- 2 \sqrt[3]{50} + 2 \sqrt[3]{-3 + \sqrt{29}} + \sqrt[3]{20} \left(-3 + \sqrt{29}\right)^{\frac{2}{3}}} + 4 \sqrt[3]{50} \sqrt{- 2 \sqrt[3]{50} + 2 \sqrt[3]{-3 + \sqrt{29}} + \sqrt[3]{20} \left(-3 + \sqrt{29}\right)^{\frac{2}{3}}} + 8 \sqrt{2} \sqrt{-3 + \sqrt{29}}}}{2 \sqrt[6]{-3 + \sqrt{29}} \sqrt[4]{- 2 \sqrt[3]{50} + 2 \sqrt[3]{-3 + \sqrt{29}} + \sqrt[3]{20} \left(-3 + \sqrt{29}\right)^{\frac{2}{3}}}}$$
=

4.61172985087874

$$y_{3} = -3 + \frac{\sqrt{- \frac{40}{\sqrt[3]{-60 + 20 \sqrt{29}}} + 4 + 2 \sqrt[3]{-60 + 20 \sqrt{29}}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{-60 + 20 \sqrt{29}} + 8 + \frac{40}{\sqrt[3]{-60 + 20 \sqrt{29}}} + \frac{16}{\sqrt{- \frac{40}{\sqrt[3]{-60 + 20 \sqrt{29}}} + 4 + 2 \sqrt[3]{-60 + 20 \sqrt{29}}}}}}{2}$$
=
$$-3 + \frac{\sqrt{- \frac{40}{\sqrt[3]{-60 + 20 \sqrt{29}}} + 4 + 2 \sqrt[3]{-60 + 20 \sqrt{29}}}}{2} + \frac{\sqrt{- 2 \sqrt[3]{-60 + 20 \sqrt{29}} + 8 + \frac{40}{\sqrt[3]{-60 + 20 \sqrt{29}}} + \frac{16}{\sqrt{- \frac{40}{\sqrt[3]{-60 + 20 \sqrt{29}}} + 4 + 2 \sqrt[3]{-60 + 20 \sqrt{29}}}}}}{2}$$
=

0.611729850878737

$$x_{4} = - \frac{\sqrt{- 2 \sqrt[3]{20} \left(-3 + \sqrt{29}\right)^{\frac{2}{3}} \sqrt{- 2 \sqrt[3]{50} + 2 \sqrt[3]{-3 + \sqrt{29}} + \sqrt[3]{20} \left(-3 + \sqrt{29}\right)^{\frac{2}{3}}} + 8 \sqrt[3]{-3 + \sqrt{29}} \sqrt{- 2 \sqrt[3]{50} + 2 \sqrt[3]{-3 + \sqrt{29}} + \sqrt[3]{20} \left(-3 + \sqrt{29}\right)^{\frac{2}{3}}} + 4 \sqrt[3]{50} \sqrt{- 2 \sqrt[3]{50} + 2 \sqrt[3]{-3 + \sqrt{29}} + \sqrt[3]{20} \left(-3 + \sqrt{29}\right)^{\frac{2}{3}}} + 8 \sqrt{2} \sqrt{-3 + \sqrt{29}}}}{2 \sqrt[6]{-3 + \sqrt{29}} \sqrt[4]{- 2 \sqrt[3]{50} + 2 \sqrt[3]{-3 + \sqrt{29}} + \sqrt[3]{20} \left(-3 + \sqrt{29}\right)^{\frac{2}{3}}}} + \frac{\sqrt{2} \sqrt{- 2 \sqrt[3]{50} + 2 \sqrt[3]{-3 + \sqrt{29}} + \sqrt[3]{20} \left(-3 + \sqrt{29}\right)^{\frac{2}{3}}}}{2 \sqrt[6]{-3 + \sqrt{29}}} + 1$$
=
$$- \frac{\sqrt{- 2 \sqrt[3]{20} \left(-3 + \sqrt{29}\right)^{\frac{2}{3}} \sqrt{- 2 \sqrt[3]{50} + 2 \sqrt[3]{-3 + \sqrt{29}} + \sqrt[3]{20} \left(-3 + \sqrt{29}\right)^{\frac{2}{3}}} + 8 \sqrt[3]{-3 + \sqrt{29}} \sqrt{- 2 \sqrt[3]{50} + 2 \sqrt[3]{-3 + \sqrt{29}} + \sqrt[3]{20} \left(-3 + \sqrt{29}\right)^{\frac{2}{3}}} + 4 \sqrt[3]{50} \sqrt{- 2 \sqrt[3]{50} + 2 \sqrt[3]{-3 + \sqrt{29}} + \sqrt[3]{20} \left(-3 + \sqrt{29}\right)^{\frac{2}{3}}} + 8 \sqrt{2} \sqrt{-3 + \sqrt{29}}}}{2 \sqrt[6]{-3 + \sqrt{29}} \sqrt[4]{- 2 \sqrt[3]{50} + 2 \sqrt[3]{-3 + \sqrt{29}} + \sqrt[3]{20} \left(-3 + \sqrt{29}\right)^{\frac{2}{3}}}} + \frac{\sqrt{2} \sqrt{- 2 \sqrt[3]{50} + 2 \sqrt[3]{-3 + \sqrt{29}} + \sqrt[3]{20} \left(-3 + \sqrt{29}\right)^{\frac{2}{3}}}}{2 \sqrt[6]{-3 + \sqrt{29}}} + 1$$
=

-2.13814888945494

$$y_{4} = - \frac{\sqrt{- 2 \sqrt[3]{-60 + 20 \sqrt{29}} + 8 + \frac{40}{\sqrt[3]{-60 + 20 \sqrt{29}}} + \frac{16}{\sqrt{- \frac{40}{\sqrt[3]{-60 + 20 \sqrt{29}}} + 4 + 2 \sqrt[3]{-60 + 20 \sqrt{29}}}}}}{2} - 3 + \frac{\sqrt{- \frac{40}{\sqrt[3]{-60 + 20 \sqrt{29}}} + 4 + 2 \sqrt[3]{-60 + 20 \sqrt{29}}}}{2}$$
=
$$- \frac{\sqrt{- 2 \sqrt[3]{-60 + 20 \sqrt{29}} + 8 + \frac{40}{\sqrt[3]{-60 + 20 \sqrt{29}}} + \frac{16}{\sqrt{- \frac{40}{\sqrt[3]{-60 + 20 \sqrt{29}}} + 4 + 2 \sqrt[3]{-60 + 20 \sqrt{29}}}}}}{2} - 3 + \frac{\sqrt{- \frac{40}{\sqrt[3]{-60 + 20 \sqrt{29}}} + 4 + 2 \sqrt[3]{-60 + 20 \sqrt{29}}}}{2}$$
=

-6.13814888945494