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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+6x^2-9x+66x-99)-180=0

We get rid of parentheses

6x^2-9x+66x-99-180=0

We add all the numbers together, and all the variables

6x^2+57x-279=0

a = 6; b = 57; c = -279;
Δ = b2-4ac
Δ = 572-4·6·(-279)
Δ = 9945
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:

$\sqrt{\Delta}=\sqrt{9945}=\sqrt{9*1105}=\sqrt{9}*\sqrt{1105}=3\sqrt{1105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(57)-3\sqrt{1105}}{2*6}=\frac{-57-3\sqrt{1105}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(57)+3\sqrt{1105}}{2*6}=\frac{-57+3\sqrt{1105}}{12}
$