x^2+20x+75=375

Solution for x^2+20x+75=375 equation:

x^2+20x+75=375

We move all terms to the left:

x^2+20x+75-(375)=0

We add all the numbers together, and all the variables

x^2+20x-300=0

a = 1; b = 20; c = -300;
Δ = b2-4ac
Δ = 202-4·1·(-300)
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-40}{2*1}=\frac{-60}{2}
=-30
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+40}{2*1}=\frac{20}{2}
=10
$