.5x(x-8)=120

Solution for .5x(x-8)=120 equation:

.5x(x-8)=120

We move all terms to the left:

.5x(x-8)-(120)=0

We multiply parentheses

x^2-8x-120=0

a = 1; b = -8; c = -120;
Δ = b2-4ac
Δ = -82-4·1·(-120)
Δ = 544
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:

$\sqrt{\Delta}=\sqrt{544}=\sqrt{16*34}=\sqrt{16}*\sqrt{34}=4\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{34}}{2*1}=\frac{8-4\sqrt{34}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{34}}{2*1}=\frac{8+4\sqrt{34}}{2}
$