y^2+30^2=38^2

Solution for y^2+30^2=38^2 equation:

y^2+30^2=38^2

We move all terms to the left:

y^2+30^2-(38^2)=0

We add all the numbers together, and all the variables

y^2-544=0

a = 1; b = 0; c = -544;
Δ = b2-4ac
Δ = 02-4·1·(-544)
Δ = 2176
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:

$\sqrt{\Delta}=\sqrt{2176}=\sqrt{64*34}=\sqrt{64}*\sqrt{34}=8\sqrt{34}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{34}}{2*1}=\frac{0-8\sqrt{34}}{2}
=-\frac{8\sqrt{34}}{2}
=-4\sqrt{34}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{34}}{2*1}=\frac{0+8\sqrt{34}}{2}
=\frac{8\sqrt{34}}{2}
=4\sqrt{34}
$