30^2+b^2=78^2

Solution for 30^2+b^2=78^2 equation:

30^2+b^2=78^2

We move all terms to the left:

30^2+b^2-(78^2)=0

We add all the numbers together, and all the variables

b^2-5184=0

a = 1; b = 0; c = -5184;
Δ = b2-4ac
Δ = 02-4·1·(-5184)
Δ = 20736
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{20736}=144$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-144}{2*1}=\frac{-144}{2}
=-72
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+144}{2*1}=\frac{144}{2}
=72
$