x+(x+11)(3x-36)=180

Solution for x+(x+11)(3x-36)=180 equation:

x+(x+11)(3x-36)=180

We move all terms to the left:

x+(x+11)(3x-36)-(180)=0

We multiply parentheses ..

(+3x^2-36x+33x-396)+x-180=0

We get rid of parentheses

3x^2-36x+33x+x-396-180=0

We add all the numbers together, and all the variables

3x^2-2x-576=0

a = 3; b = -2; c = -576;
Δ = b2-4ac
Δ = -22-4·3·(-576)
Δ = 6916
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:

$\sqrt{\Delta}=\sqrt{6916}=\sqrt{4*1729}=\sqrt{4}*\sqrt{1729}=2\sqrt{1729}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{1729}}{2*3}=\frac{2-2\sqrt{1729}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{1729}}{2*3}=\frac{2+2\sqrt{1729}}{6}
$