(2x+5)(2x+5)-12=0

Solution for (2x+5)(2x+5)-12=0 equation:

(2x+5)(2x+5)-12=0

We multiply parentheses ..

(+4x^2+10x+10x+25)-12=0

We get rid of parentheses

4x^2+10x+10x+25-12=0

We add all the numbers together, and all the variables

4x^2+20x+13=0

a = 4; b = 20; c = +13;
Δ = b2-4ac
Δ = 202-4·4·13
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*4}=\frac{-20-8\sqrt{3}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+8\sqrt{3}}{2*4}=\frac{-20+8\sqrt{3}}{8}
$