84^2+b^2=91^2

Solution for 84^2+b^2=91^2 equation:

84^2+b^2=91^2

We move all terms to the left:

84^2+b^2-(91^2)=0

We add all the numbers together, and all the variables

b^2-1225=0

a = 1; b = 0; c = -1225;
Δ = b2-4ac
Δ = 02-4·1·(-1225)
Δ = 4900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4900}=70$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-70}{2*1}=\frac{-70}{2}
=-35
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+70}{2*1}=\frac{70}{2}
=35
$