x^2+8x-24=15

Solution for x^2+8x-24=15 equation:

x^2+8x-24=15

We move all terms to the left:

x^2+8x-24-(15)=0

We add all the numbers together, and all the variables

x^2+8x-39=0

a = 1; b = 8; c = -39;
Δ = b2-4ac
Δ = 82-4·1·(-39)
Δ = 220
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:

$\sqrt{\Delta}=\sqrt{220}=\sqrt{4*55}=\sqrt{4}*\sqrt{55}=2\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{55}}{2*1}=\frac{-8-2\sqrt{55}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{55}}{2*1}=\frac{-8+2\sqrt{55}}{2}
$