y^2-8=23

Solution for y^2-8=23 equation:

y^2-8=23

We move all terms to the left:

y^2-8-(23)=0

We add all the numbers together, and all the variables

y^2-31=0

a = 1; b = 0; c = -31;
Δ = b2-4ac
Δ = 02-4·1·(-31)
Δ = 124
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:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{31}}{2*1}=\frac{0-2\sqrt{31}}{2}
=-\frac{2\sqrt{31}}{2}
=-\sqrt{31}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{31}}{2*1}=\frac{0+2\sqrt{31}}{2}
=\frac{2\sqrt{31}}{2}
=\sqrt{31}
$