(x-10)x=120

Solution for (x-10)x=120 equation:

(x-10)x=120

We move all terms to the left:

(x-10)x-(120)=0

We multiply parentheses

x^2-10x-120=0

a = 1; b = -10; c = -120;
Δ = b2-4ac
Δ = -102-4·1·(-120)
Δ = 580
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:

$\sqrt{\Delta}=\sqrt{580}=\sqrt{4*145}=\sqrt{4}*\sqrt{145}=2\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{145}}{2*1}=\frac{10-2\sqrt{145}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{145}}{2*1}=\frac{10+2\sqrt{145}}{2}
$