(2x+3)(x-6)=180

Solution for (2x+3)(x-6)=180 equation:

(2x+3)(x-6)=180

We move all terms to the left:

(2x+3)(x-6)-(180)=0

We multiply parentheses ..

(+2x^2-12x+3x-18)-180=0

We get rid of parentheses

2x^2-12x+3x-18-180=0

We add all the numbers together, and all the variables

2x^2-9x-198=0

a = 2; b = -9; c = -198;
Δ = b2-4ac
Δ = -92-4·2·(-198)
Δ = 1665
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:

$\sqrt{\Delta}=\sqrt{1665}=\sqrt{9*185}=\sqrt{9}*\sqrt{185}=3\sqrt{185}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{185}}{2*2}=\frac{9-3\sqrt{185}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{185}}{2*2}=\frac{9+3\sqrt{185}}{4}
$