Y=2x2-31

Solution for Y=2x2-31 equation:

=2Y^2-31

We move all terms to the left:

-(2Y^2-31)=0

We get rid of parentheses

-2Y^2+31=0

a = -2; b = 0; c = +31;
Δ = b2-4ac
Δ = 02-4·(-2)·31
Δ = 248
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:

$\sqrt{\Delta}=\sqrt{248}=\sqrt{4*62}=\sqrt{4}*\sqrt{62}=2\sqrt{62}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{62}}{2*-2}=\frac{0-2\sqrt{62}}{-4}
=-\frac{2\sqrt{62}}{-4}
=-\frac{\sqrt{62}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{62}}{2*-2}=\frac{0+2\sqrt{62}}{-4}
=\frac{2\sqrt{62}}{-4}
=\frac{\sqrt{62}}{-2}
$