75^2+b^2=85^2

Solution for 75^2+b^2=85^2 equation:

75^2+b^2=85^2

We move all terms to the left:

75^2+b^2-(85^2)=0

We add all the numbers together, and all the variables

b^2-1600=0

a = 1; b = 0; c = -1600;
Δ = b2-4ac
Δ = 02-4·1·(-1600)
Δ = 6400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6400}=80$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-80}{2*1}=\frac{-80}{2}
=-40
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+80}{2*1}=\frac{80}{2}
=40
$