(2x+5)(3x-33)=180

Solution for (2x+5)(3x-33)=180 equation:

(2x+5)(3x-33)=180

We move all terms to the left:

(2x+5)(3x-33)-(180)=0

We multiply parentheses ..

(+6x^2-66x+15x-165)-180=0

We get rid of parentheses

6x^2-66x+15x-165-180=0

We add all the numbers together, and all the variables

6x^2-51x-345=0

a = 6; b = -51; c = -345;
Δ = b2-4ac
Δ = -512-4·6·(-345)
Δ = 10881
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:

$\sqrt{\Delta}=\sqrt{10881}=\sqrt{9*1209}=\sqrt{9}*\sqrt{1209}=3\sqrt{1209}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-51)-3\sqrt{1209}}{2*6}=\frac{51-3\sqrt{1209}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+3\sqrt{1209}}{2*6}=\frac{51+3\sqrt{1209}}{12}
$