x(x-10)=150

Solution for x(x-10)=150 equation:

x(x-10)=150

We move all terms to the left:

x(x-10)-(150)=0

We multiply parentheses

x^2-10x-150=0

a = 1; b = -10; c = -150;
Δ = b2-4ac
Δ = -102-4·1·(-150)
Δ = 700
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:

$\sqrt{\Delta}=\sqrt{700}=\sqrt{100*7}=\sqrt{100}*\sqrt{7}=10\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10\sqrt{7}}{2*1}=\frac{10-10\sqrt{7}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10\sqrt{7}}{2*1}=\frac{10+10\sqrt{7}}{2}
$