Move right part of the equation to
left part with negative sign.
The equation is transformed from
$$\left(x - 3\right) \left(x + 4\right) = x \left(1 - x\right)$$
to
$$- x \left(1 - x\right) + \left(x - 3\right) \left(x + 4\right) = 0$$
Expand the expression in the equation
$$- x \left(1 - x\right) + \left(x - 3\right) \left(x + 4\right) = 0$$
We get the quadratic equation
$$2 x^{2} - 12 = 0$$
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
$$a = 2$$
$$b = 0$$
$$c = -12$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (2) * (-12) = 96
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \sqrt{6}$$
$$x_{2} = - \sqrt{6}$$