(15+x)(20+x)=375

Solution for (15+x)(20+x)=375 equation:

(15+x)(20+x)=375

We move all terms to the left:

(15+x)(20+x)-(375)=0

We add all the numbers together, and all the variables

(x+15)(x+20)-375=0

We multiply parentheses ..

(+x^2+20x+15x+300)-375=0

We get rid of parentheses

x^2+20x+15x+300-375=0

We add all the numbers together, and all the variables

x^2+35x-75=0

a = 1; b = 35; c = -75;
Δ = b2-4ac
Δ = 352-4·1·(-75)
Δ = 1525
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:

$\sqrt{\Delta}=\sqrt{1525}=\sqrt{25*61}=\sqrt{25}*\sqrt{61}=5\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-5\sqrt{61}}{2*1}=\frac{-35-5\sqrt{61}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+5\sqrt{61}}{2*1}=\frac{-35+5\sqrt{61}}{2}
$