13^2+b^2=85^2

Solution for 13^2+b^2=85^2 equation:

13^2+b^2=85^2

We move all terms to the left:

13^2+b^2-(85^2)=0

We add all the numbers together, and all the variables

b^2-7056=0

a = 1; b = 0; c = -7056;
Δ = b2-4ac
Δ = 02-4·1·(-7056)
Δ = 28224
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{28224}=168$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-168}{2*1}=\frac{-168}{2}
=-84
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+168}{2*1}=\frac{168}{2}
=84
$