3.5^2+12^2=y^2

Solution for 3.5^2+12^2=y^2 equation:

3.5^2+12^2=y^2

We move all terms to the left:

3.5^2+12^2-(y^2)=0

We add all the numbers together, and all the variables

-1y^2+156.25=0

a = -1; b = 0; c = +156.25;
Δ = b2-4ac
Δ = 02-4·(-1)·156.25
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-25}{2*-1}=\frac{-25}{-2}
=12+1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+25}{2*-1}=\frac{25}{-2}
=-12+1/2
$