(x+2)(x+8)=24

Solution for (x+2)(x+8)=24 equation:

(x+2)(x+8)=24

We move all terms to the left:

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

We multiply parentheses ..

(+x^2+8x+2x+16)-24=0

We get rid of parentheses

x^2+8x+2x+16-24=0

We add all the numbers together, and all the variables

x^2+10x-8=0

a = 1; b = 10; c = -8;
Δ = b2-4ac
Δ = 102-4·1·(-8)
Δ = 132
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:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{33}}{2*1}=\frac{-10-2\sqrt{33}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{33}}{2*1}=\frac{-10+2\sqrt{33}}{2}
$