12(9^2x+3)=180

Solution for 12(9^2x+3)=180 equation:

12(9^2x+3)=180

We move all terms to the left:

12(9^2x+3)-(180)=0

We multiply parentheses

108x^2+36-180=0

We add all the numbers together, and all the variables

108x^2-144=0

a = 108; b = 0; c = -144;
Δ = b2-4ac
Δ = 02-4·108·(-144)
Δ = 62208
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:

$\sqrt{\Delta}=\sqrt{62208}=\sqrt{20736*3}=\sqrt{20736}*\sqrt{3}=144\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-144\sqrt{3}}{2*108}=\frac{0-144\sqrt{3}}{216}
=-\frac{144\sqrt{3}}{216}
=-\frac{2\sqrt{3}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+144\sqrt{3}}{2*108}=\frac{0+144\sqrt{3}}{216}
=\frac{144\sqrt{3}}{216}
=\frac{2\sqrt{3}}{3}
$