12x^2-72x-24=0

Solution for 12x^2-72x-24=0 equation:

12x^2-72x-24=0

a = 12; b = -72; c = -24;
Δ = b2-4ac
Δ = -722-4·12·(-24)
Δ = 6336
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:

$\sqrt{\Delta}=\sqrt{6336}=\sqrt{576*11}=\sqrt{576}*\sqrt{11}=24\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-24\sqrt{11}}{2*12}=\frac{72-24\sqrt{11}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+24\sqrt{11}}{2*12}=\frac{72+24\sqrt{11}}{24}
$