y2-44=102

Solution for y2-44=102 equation:

y2-44=102

We move all terms to the left:

y2-44-(102)=0

We add all the numbers together, and all the variables

y^2-146=0

a = 1; b = 0; c = -146;
Δ = b2-4ac
Δ = 02-4·1·(-146)
Δ = 584
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:

$\sqrt{\Delta}=\sqrt{584}=\sqrt{4*146}=\sqrt{4}*\sqrt{146}=2\sqrt{146}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{146}}{2*1}=\frac{0-2\sqrt{146}}{2}
=-\frac{2\sqrt{146}}{2}
=-\sqrt{146}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{146}}{2*1}=\frac{0+2\sqrt{146}}{2}
=\frac{2\sqrt{146}}{2}
=\sqrt{146}
$