(2x+1)(5x+5)+90=180

Solution for (2x+1)(5x+5)+90=180 equation:

(2x+1)(5x+5)+90=180

We move all terms to the left:

(2x+1)(5x+5)+90-(180)=0

We add all the numbers together, and all the variables

(2x+1)(5x+5)-90=0

We multiply parentheses ..

(+10x^2+10x+5x+5)-90=0

We get rid of parentheses

10x^2+10x+5x+5-90=0

We add all the numbers together, and all the variables

10x^2+15x-85=0

a = 10; b = 15; c = -85;
Δ = b2-4ac
Δ = 152-4·10·(-85)
Δ = 3625
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:

$\sqrt{\Delta}=\sqrt{3625}=\sqrt{25*145}=\sqrt{25}*\sqrt{145}=5\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-5\sqrt{145}}{2*10}=\frac{-15-5\sqrt{145}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+5\sqrt{145}}{2*10}=\frac{-15+5\sqrt{145}}{20}
$