Move right part of the equation to
left part with negative sign.
The equation is transformed from
$$20 x^{2} - 21 x + 22 = 17 x^{2} - 75 x - 218$$
to
$$\left(- 17 x^{2} + 75 x + 218\right) + \left(20 x^{2} - 21 x + 22\right) = 0$$
This equation is of the form
$$a*x^2 + b*x + c = 0$$
A quadratic equation can be solved using the discriminant
The roots of the quadratic equation:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where $D = b^2 - 4 a c$ is the discriminant.
Because
$$a = 3$$
$$b = 54$$
$$c = 240$$
, then
$$D = b^2 - 4 * a * c = $$
$$\left(-1\right) 3 \cdot 4 \cdot 240 + 54^{2} = 36$$
Because D > 0, then the equation has two roots.
$$x_1 = \frac{(-b + \sqrt{D})}{2 a}$$
$$x_2 = \frac{(-b - \sqrt{D})}{2 a}$$
or
$$x_{1} = -8$$
Simplify$$x_{2} = -10$$
Simplify