(x^3)+10(x^2)+7x-18=0 equation

Given the equation:
$$\left(7 x + \left(x^{3} + 10 x^{2}\right)\right) - 18 = 0$$
transform
$$\left(7 x + \left(\left(10 x^{2} + \left(x^{3} - 1\right)\right) - 10\right)\right) - 7 = 0$$
or
$$\left(7 x + \left(\left(10 x^{2} + \left(x^{3} - 1^{3}\right)\right) - 10 \cdot 1^{2}\right)\right) - 7 = 0$$
$$7 \left(x - 1\right) + \left(10 \left(x^{2} - 1^{2}\right) + \left(x^{3} - 1^{3}\right)\right) = 0$$
$$7 \left(x - 1\right) + \left(\left(x - 1\right) \left(\left(x^{2} + x\right) + 1^{2}\right) + 10 \left(x - 1\right) \left(x + 1\right)\right) = 0$$
Take common factor -1 + x from the equation
we get:
$$\left(x - 1\right) \left(\left(10 \left(x + 1\right) + \left(\left(x^{2} + x\right) + 1^{2}\right)\right) + 7\right) = 0$$
or
$$\left(x - 1\right) \left(x^{2} + 11 x + 18\right) = 0$$
then:
$$x_{1} = 1$$
and also
we get the equation
$$x^{2} + 11 x + 18 = 0$$
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:
$$x_{2} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{3} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 1$$
$$b = 11$$
$$c = 18$$
, then

D = b^2 - 4 * a * c = 

(11)^2 - 4 * (1) * (18) = 49

Because D > 0, then the equation has two roots.

x2 = (-b + sqrt(D)) / (2*a)

x3 = (-b - sqrt(D)) / (2*a)

or
$$x_{2} = -2$$
$$x_{3} = -9$$
The final answer for x^3 + 10*x^2 + 7*x - 18 = 0:
$$x_{1} = 1$$
$$x_{2} = -2$$
$$x_{3} = -9$$