36^2+b^2=100*100

Solution for 36^2+b^2=100*100 equation:

36^2+b^2=100*100

We move all terms to the left:

36^2+b^2-(100*100)=0

We add all the numbers together, and all the variables

b^2+36^2-10000=0

We add all the numbers together, and all the variables

b^2-8704=0

a = 1; b = 0; c = -8704;
Δ = b2-4ac
Δ = 02-4·1·(-8704)
Δ = 34816
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:

$\sqrt{\Delta}=\sqrt{34816}=\sqrt{1024*34}=\sqrt{1024}*\sqrt{34}=32\sqrt{34}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-32\sqrt{34}}{2*1}=\frac{0-32\sqrt{34}}{2}
=-\frac{32\sqrt{34}}{2}
=-16\sqrt{34}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+32\sqrt{34}}{2*1}=\frac{0+32\sqrt{34}}{2}
=\frac{32\sqrt{34}}{2}
=16\sqrt{34}
$