b^2=50^2

Solution for b^2=50^2 equation:

b^2=50^2

We move all terms to the left:

b^2-(50^2)=0

We add all the numbers together, and all the variables

b^2-2500=0

a = 1; b = 0; c = -2500;
Δ = b2-4ac
Δ = 02-4·1·(-2500)
Δ = 10000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10000}=100$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-100}{2*1}=\frac{-100}{2}
=-50
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+100}{2*1}=\frac{100}{2}
=50
$