(3x-9)(x+15)+90=180

Solution for (3x-9)(x+15)+90=180 equation:

(3x-9)(x+15)+90=180

We move all terms to the left:

(3x-9)(x+15)+90-(180)=0

We add all the numbers together, and all the variables

(3x-9)(x+15)-90=0

We multiply parentheses ..

(+3x^2+45x-9x-135)-90=0

We get rid of parentheses

3x^2+45x-9x-135-90=0

We add all the numbers together, and all the variables

3x^2+36x-225=0

a = 3; b = 36; c = -225;
Δ = b2-4ac
Δ = 362-4·3·(-225)
Δ = 3996
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3996}=\sqrt{36*111}=\sqrt{36}*\sqrt{111}=6\sqrt{111}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-6\sqrt{111}}{2*3}=\frac{-36-6\sqrt{111}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+6\sqrt{111}}{2*3}=\frac{-36+6\sqrt{111}}{6}
$