(9x-2)(3x+6)=180

Solution for (9x-2)(3x+6)=180 equation:

(9x-2)(3x+6)=180

We move all terms to the left:

(9x-2)(3x+6)-(180)=0

We multiply parentheses ..

(+27x^2+54x-6x-12)-180=0

We get rid of parentheses

27x^2+54x-6x-12-180=0

We add all the numbers together, and all the variables

27x^2+48x-192=0

a = 27; b = 48; c = -192;
Δ = b2-4ac
Δ = 482-4·27·(-192)
Δ = 23040
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:

$\sqrt{\Delta}=\sqrt{23040}=\sqrt{2304*10}=\sqrt{2304}*\sqrt{10}=48\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-48\sqrt{10}}{2*27}=\frac{-48-48\sqrt{10}}{54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+48\sqrt{10}}{2*27}=\frac{-48+48\sqrt{10}}{54}
$