(x+12)(x-9)+x=180

Solution for (x+12)(x-9)+x=180 equation:

(x+12)(x-9)+x=180

We move all terms to the left:

(x+12)(x-9)+x-(180)=0

We add all the numbers together, and all the variables

x+(x+12)(x-9)-180=0

We multiply parentheses ..

(+x^2-9x+12x-108)+x-180=0

We get rid of parentheses

x^2-9x+12x+x-108-180=0

We add all the numbers together, and all the variables

x^2+4x-288=0

a = 1; b = 4; c = -288;
Δ = b2-4ac
Δ = 42-4·1·(-288)
Δ = 1168
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:

$\sqrt{\Delta}=\sqrt{1168}=\sqrt{16*73}=\sqrt{16}*\sqrt{73}=4\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{73}}{2*1}=\frac{-4-4\sqrt{73}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{73}}{2*1}=\frac{-4+4\sqrt{73}}{2}
$