120=2x^2+10

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

120=2x^2+10

We move all terms to the left:

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

We get rid of parentheses

-2x^2-10+120=0

We add all the numbers together, and all the variables

-2x^2+110=0

a = -2; b = 0; c = +110;
Δ = b2-4ac
Δ = 02-4·(-2)·110
Δ = 880
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:

$\sqrt{\Delta}=\sqrt{880}=\sqrt{16*55}=\sqrt{16}*\sqrt{55}=4\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{55}}{2*-2}=\frac{0-4\sqrt{55}}{-4}
=-\frac{4\sqrt{55}}{-4}
=-\frac{\sqrt{55}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{55}}{2*-2}=\frac{0+4\sqrt{55}}{-4}
=\frac{4\sqrt{55}}{-4}
=\frac{\sqrt{55}}{-1}
$