x(x-40)=375

Solution for x(x-40)=375 equation:

x(x-40)=375

We move all terms to the left:

x(x-40)-(375)=0

We multiply parentheses

x^2-40x-375=0

a = 1; b = -40; c = -375;
Δ = b2-4ac
Δ = -402-4·1·(-375)
Δ = 3100
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:

$\sqrt{\Delta}=\sqrt{3100}=\sqrt{100*31}=\sqrt{100}*\sqrt{31}=10\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-10\sqrt{31}}{2*1}=\frac{40-10\sqrt{31}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+10\sqrt{31}}{2*1}=\frac{40+10\sqrt{31}}{2}
$