x^2+24x-288=0

Solution for x^2+24x-288=0 equation:

x^2+24x-288=0

a = 1; b = 24; c = -288;
Δ = b2-4ac
Δ = 242-4·1·(-288)
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{-(24)-24\sqrt{3}}{2*1}=\frac{-24-24\sqrt{3}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24\sqrt{3}}{2*1}=\frac{-24+24\sqrt{3}}{2}
$