(2x+5)(2x+2)=26

Solution for (2x+5)(2x+2)=26 equation:

(2x+5)(2x+2)=26

We move all terms to the left:

(2x+5)(2x+2)-(26)=0

We multiply parentheses ..

(+4x^2+4x+10x+10)-26=0

We get rid of parentheses

4x^2+4x+10x+10-26=0

We add all the numbers together, and all the variables

4x^2+14x-16=0

a = 4; b = 14; c = -16;
Δ = b2-4ac
Δ = 142-4·4·(-16)
Δ = 452
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:

$\sqrt{\Delta}=\sqrt{452}=\sqrt{4*113}=\sqrt{4}*\sqrt{113}=2\sqrt{113}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{113}}{2*4}=\frac{-14-2\sqrt{113}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{113}}{2*4}=\frac{-14+2\sqrt{113}}{8}
$