y^2-2=32

Solution for y^2-2=32 equation:

y^2-2=32

We move all terms to the left:

y^2-2-(32)=0

We add all the numbers together, and all the variables

y^2-34=0

a = 1; b = 0; c = -34;
Δ = b2-4ac
Δ = 02-4·1·(-34)
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{34}}{2*1}=\frac{0-2\sqrt{34}}{2}
=-\frac{2\sqrt{34}}{2}
=-\sqrt{34}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{34}}{2*1}=\frac{0+2\sqrt{34}}{2}
=\frac{2\sqrt{34}}{2}
=\sqrt{34}
$