6^2+b^2=13^2

Solution for 6^2+b^2=13^2 equation:

6^2+b^2=13^2

We move all terms to the left:

6^2+b^2-(13^2)=0

We add all the numbers together, and all the variables

b^2-133=0

a = 1; b = 0; c = -133;
Δ = b2-4ac
Δ = 02-4·1·(-133)
Δ = 532
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{532}=\sqrt{4*133}=\sqrt{4}*\sqrt{133}=2\sqrt{133}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{133}}{2*1}=\frac{0-2\sqrt{133}}{2}
=-\frac{2\sqrt{133}}{2}
=-\sqrt{133}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{133}}{2*1}=\frac{0+2\sqrt{133}}{2}
=\frac{2\sqrt{133}}{2}
=\sqrt{133}
$