X(x-25)=150

Solution for X(x-25)=150 equation:

X(X-25)=150

We move all terms to the left:

X(X-25)-(150)=0

We multiply parentheses

X^2-25X-150=0

a = 1; b = -25; c = -150;
Δ = b2-4ac
Δ = -252-4·1·(-150)
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-35}{2*1}=\frac{-10}{2}
=-5
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+35}{2*1}=\frac{60}{2}
=30
$