360=10x^2+120

Solution for 360=10x^2+120 equation:

360=10x^2+120

We move all terms to the left:

360-(10x^2+120)=0

We get rid of parentheses

-10x^2-120+360=0

We add all the numbers together, and all the variables

-10x^2+240=0

a = -10; b = 0; c = +240;
Δ = b2-4ac
Δ = 02-4·(-10)·240
Δ = 9600
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:

$\sqrt{\Delta}=\sqrt{9600}=\sqrt{1600*6}=\sqrt{1600}*\sqrt{6}=40\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{6}}{2*-10}=\frac{0-40\sqrt{6}}{-20}
=-\frac{40\sqrt{6}}{-20}
=-\frac{2\sqrt{6}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{6}}{2*-10}=\frac{0+40\sqrt{6}}{-20}
=\frac{40\sqrt{6}}{-20}
=\frac{2\sqrt{6}}{-1}
$