12x^2-144x+36=0

Solution for 12x^2-144x+36=0 equation:

12x^2-144x+36=0

a = 12; b = -144; c = +36;
Δ = b2-4ac
Δ = -1442-4·12·36
Δ = 19008
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:

$\sqrt{\Delta}=\sqrt{19008}=\sqrt{576*33}=\sqrt{576}*\sqrt{33}=24\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-24\sqrt{33}}{2*12}=\frac{144-24\sqrt{33}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+24\sqrt{33}}{2*12}=\frac{144+24\sqrt{33}}{24}
$