6x^2-72x+144=0

Solution for 6x^2-72x+144=0 equation:

6x^2-72x+144=0

a = 6; b = -72; c = +144;
Δ = b2-4ac
Δ = -722-4·6·144
Δ = 1728
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:

$\sqrt{\Delta}=\sqrt{1728}=\sqrt{576*3}=\sqrt{576}*\sqrt{3}=24\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-24\sqrt{3}}{2*6}=\frac{72-24\sqrt{3}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+24\sqrt{3}}{2*6}=\frac{72+24\sqrt{3}}{12}
$