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 add all the numbers together, and all the variables

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 = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-5}{2*1}=\frac{20}{2}
=10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+5}{2*1}=\frac{30}{2}
=15
$