(x+34)(2x+2)=180

Solution for (x+34)(2x+2)=180 equation:

(x+34)(2x+2)=180

We move all terms to the left:

(x+34)(2x+2)-(180)=0

We multiply parentheses ..

(+2x^2+2x+68x+68)-180=0

We get rid of parentheses

2x^2+2x+68x+68-180=0

We add all the numbers together, and all the variables

2x^2+70x-112=0

a = 2; b = 70; c = -112;
Δ = b2-4ac
Δ = 702-4·2·(-112)
Δ = 5796
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:

$\sqrt{\Delta}=\sqrt{5796}=\sqrt{36*161}=\sqrt{36}*\sqrt{161}=6\sqrt{161}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(70)-6\sqrt{161}}{2*2}=\frac{-70-6\sqrt{161}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(70)+6\sqrt{161}}{2*2}=\frac{-70+6\sqrt{161}}{4}
$