3x(4x-18)=180

Solution for 3x(4x-18)=180 equation:

3x(4x-18)=180

We move all terms to the left:

3x(4x-18)-(180)=0

We multiply parentheses

12x^2-54x-180=0

a = 12; b = -54; c = -180;
Δ = b2-4ac
Δ = -542-4·12·(-180)
Δ = 11556
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:

$\sqrt{\Delta}=\sqrt{11556}=\sqrt{36*321}=\sqrt{36}*\sqrt{321}=6\sqrt{321}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-6\sqrt{321}}{2*12}=\frac{54-6\sqrt{321}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+6\sqrt{321}}{2*12}=\frac{54+6\sqrt{321}}{24}
$