(2x+5)(2x-6)=26

Solution for (2x+5)(2x-6)=26 equation:

(2x+5)(2x-6)=26

We move all terms to the left:

(2x+5)(2x-6)-(26)=0

We multiply parentheses ..

(+4x^2-12x+10x-30)-26=0

We get rid of parentheses

4x^2-12x+10x-30-26=0

We add all the numbers together, and all the variables

4x^2-2x-56=0

a = 4; b = -2; c = -56;
Δ = b2-4ac
Δ = -22-4·4·(-56)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-30}{2*4}=\frac{-28}{8}
=-3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+30}{2*4}=\frac{32}{8}
=4
$