(2x+4)(x+26)=180

Solution for (2x+4)(x+26)=180 equation:

(2x+4)(x+26)=180

We move all terms to the left:

(2x+4)(x+26)-(180)=0

We multiply parentheses ..

(+2x^2+52x+4x+104)-180=0

We get rid of parentheses

2x^2+52x+4x+104-180=0

We add all the numbers together, and all the variables

2x^2+56x-76=0

a = 2; b = 56; c = -76;
Δ = b2-4ac
Δ = 562-4·2·(-76)
Δ = 3744
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:

$\sqrt{\Delta}=\sqrt{3744}=\sqrt{144*26}=\sqrt{144}*\sqrt{26}=12\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-12\sqrt{26}}{2*2}=\frac{-56-12\sqrt{26}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+12\sqrt{26}}{2*2}=\frac{-56+12\sqrt{26}}{4}
$