(2x+2)(x+34)=90

Solution for (2x+2)(x+34)=90 equation:

(2x+2)(x+34)=90

We move all terms to the left:

(2x+2)(x+34)-(90)=0

We multiply parentheses ..

(+2x^2+68x+2x+68)-90=0

We get rid of parentheses

2x^2+68x+2x+68-90=0

We add all the numbers together, and all the variables

2x^2+70x-22=0

a = 2; b = 70; c = -22;
Δ = b2-4ac
Δ = 702-4·2·(-22)
Δ = 5076
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:

$\sqrt{\Delta}=\sqrt{5076}=\sqrt{36*141}=\sqrt{36}*\sqrt{141}=6\sqrt{141}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(70)-6\sqrt{141}}{2*2}=\frac{-70-6\sqrt{141}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(70)+6\sqrt{141}}{2*2}=\frac{-70+6\sqrt{141}}{4}
$