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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

3x^2+16x-192=0

a = 3; b = 16; c = -192;
Δ = b2-4ac
Δ = 162-4·3·(-192)
Δ = 2560
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:

$\sqrt{\Delta}=\sqrt{2560}=\sqrt{256*10}=\sqrt{256}*\sqrt{10}=16\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16\sqrt{10}}{2*3}=\frac{-16-16\sqrt{10}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16\sqrt{10}}{2*3}=\frac{-16+16\sqrt{10}}{6}
$