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х^2=7у+2; х^2+2=7у+у^2

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The solution

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 2          
x  = 7*y + 2
$$x^{2} = 7 y + 2$$
 2              2
x  + 2 = 7*y + y 
$$x^{2} + 2 = y^{2} + 7 y$$
x^2 + 2 = y^2 + 7*y
Rapid solution
$$x_{1} = -4$$
=
$$-4$$
=
-4

$$y_{1} = 2$$
=
$$2$$
=
2
$$x_{2} = 4$$
=
$$4$$
=
4

$$y_{2} = 2$$
=
$$2$$
=
2
$$x_{3} = - 2 \sqrt{3} i$$
=
$$- 2 \sqrt{3} i$$
=
-3.46410161513775*i

$$y_{3} = -2$$
=
$$-2$$
=
-2
$$x_{4} = 2 \sqrt{3} i$$
=
$$2 \sqrt{3} i$$
=
3.46410161513775*i

$$y_{4} = -2$$
=
$$-2$$
=
-2