100=2y^2+10

Solution for 100=2y^2+10 equation:

100=2y^2+10

We move all terms to the left:

100-(2y^2+10)=0

We get rid of parentheses

-2y^2-10+100=0

We add all the numbers together, and all the variables

-2y^2+90=0

a = -2; b = 0; c = +90;
Δ = b2-4ac
Δ = 02-4·(-2)·90
Δ = 720
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{5}}{2*-2}=\frac{0-12\sqrt{5}}{-4}
=-\frac{12\sqrt{5}}{-4}
=-\frac{3\sqrt{5}}{-1}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{5}}{2*-2}=\frac{0+12\sqrt{5}}{-4}
=\frac{12\sqrt{5}}{-4}
=\frac{3\sqrt{5}}{-1}
$