11x^2-72x-24=0

Solution for 11x^2-72x-24=0 equation:

11x^2-72x-24=0

a = 11; b = -72; c = -24;
Δ = b2-4ac
Δ = -722-4·11·(-24)
Δ = 6240
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:

$\sqrt{\Delta}=\sqrt{6240}=\sqrt{16*390}=\sqrt{16}*\sqrt{390}=4\sqrt{390}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-4\sqrt{390}}{2*11}=\frac{72-4\sqrt{390}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+4\sqrt{390}}{2*11}=\frac{72+4\sqrt{390}}{22}
$