10x=(5x^2)-120

Solution for 10x=(5x^2)-120 equation:

10x=(5x^2)-120

We move all terms to the left:

10x-((5x^2)-120)=0

We get rid of parentheses

-5x^2+10x+120=0

a = -5; b = 10; c = +120;
Δ = b2-4ac
Δ = 102-4·(-5)·120
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-50}{2*-5}=\frac{-60}{-10}
=+6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+50}{2*-5}=\frac{40}{-10}
=-4
$