Y+2x^2-5=90

Solution for Y+2x^2-5=90 equation:

+2Y^2-5=90

We move all terms to the left:

+2Y^2-5-(90)=0

We add all the numbers together, and all the variables

2Y^2-95=0

a = 2; b = 0; c = -95;
Δ = b2-4ac
Δ = 02-4·2·(-95)
Δ = 760
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:

$\sqrt{\Delta}=\sqrt{760}=\sqrt{4*190}=\sqrt{4}*\sqrt{190}=2\sqrt{190}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{190}}{2*2}=\frac{0-2\sqrt{190}}{4}
=-\frac{2\sqrt{190}}{4}
=-\frac{\sqrt{190}}{2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{190}}{2*2}=\frac{0+2\sqrt{190}}{4}
=\frac{2\sqrt{190}}{4}
=\frac{\sqrt{190}}{2}
$