2(x+5)(x+5)=24

Solution for 2(x+5)(x+5)=24 equation:

2(x+5)(x+5)=24

We move all terms to the left:

2(x+5)(x+5)-(24)=0

We multiply parentheses ..

2(+x^2+5x+5x+25)-24=0

We multiply parentheses

2x^2+10x+10x+50-24=0

We add all the numbers together, and all the variables

2x^2+20x+26=0

a = 2; b = 20; c = +26;
Δ = b2-4ac
Δ = 202-4·2·26
Δ = 192
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:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-8\sqrt{3}}{2*2}=\frac{-20-8\sqrt{3}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+8\sqrt{3}}{2*2}=\frac{-20+8\sqrt{3}}{4}
$