(15+x)(20+x)=750

Solution for (15+x)(20+x)=750 equation:

(15+x)(20+x)=750

We move all terms to the left:

(15+x)(20+x)-(750)=0

We add all the numbers together, and all the variables

(x+15)(x+20)-750=0

We multiply parentheses ..

(+x^2+20x+15x+300)-750=0

We get rid of parentheses

x^2+20x+15x+300-750=0

We add all the numbers together, and all the variables

x^2+35x-450=0

a = 1; b = 35; c = -450;
Δ = b2-4ac
Δ = 352-4·1·(-450)
Δ = 3025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3025}=55$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-55}{2*1}=\frac{-90}{2}
=-45
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+55}{2*1}=\frac{20}{2}
=10
$