(x+10)(x+15)=500

Solution for (x+10)(x+15)=500 equation:

(x+10)(x+15)=500

We move all terms to the left:

(x+10)(x+15)-(500)=0

We multiply parentheses ..

(+x^2+15x+10x+150)-500=0

We get rid of parentheses

x^2+15x+10x+150-500=0

We add all the numbers together, and all the variables

x^2+25x-350=0

a = 1; b = 25; c = -350;
Δ = b2-4ac
Δ = 252-4·1·(-350)
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-45}{2*1}=\frac{-70}{2}
=-35
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+45}{2*1}=\frac{20}{2}
=10
$