Move right part of the equation to
left part with negative sign.
The equation is transformed from
$$\left(7 x^{2} + 6 x\right) - 9 = \left(14 - x^{2}\right) - 3$$
to
$$\left(\left(x^{2} - 14\right) + 3\right) + \left(\left(7 x^{2} + 6 x\right) - 9\right) = 0$$
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 - it is the discriminant.
Because
$$a = 8$$
$$b = 6$$
$$c = -20$$
, then
D = b^2 - 4 * a * c =
(6)^2 - 4 * (8) * (-20) = 676
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \frac{5}{4}$$
$$x_{2} = -2$$