(2x+15)(2x+10)=85

Solution for (2x+15)(2x+10)=85 equation:

(2x+15)(2x+10)=85

We move all terms to the left:

(2x+15)(2x+10)-(85)=0

We multiply parentheses ..

(+4x^2+20x+30x+150)-85=0

We get rid of parentheses

4x^2+20x+30x+150-85=0

We add all the numbers together, and all the variables

4x^2+50x+65=0

a = 4; b = 50; c = +65;
Δ = b2-4ac
Δ = 502-4·4·65
Δ = 1460
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:

$\sqrt{\Delta}=\sqrt{1460}=\sqrt{4*365}=\sqrt{4}*\sqrt{365}=2\sqrt{365}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-2\sqrt{365}}{2*4}=\frac{-50-2\sqrt{365}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+2\sqrt{365}}{2*4}=\frac{-50+2\sqrt{365}}{8}
$