b^2+50b=111111.111

Solution for b^2+50b=111111.111 equation:

b^2+50b=111111.111

We move all terms to the left:

b^2+50b-(111111.111)=0

We add all the numbers together, and all the variables

b^2+50b-111111.111=0

a = 1; b = 50; c = -111111.111;
Δ = b2-4ac
Δ = 502-4·1·(-111111.111)
Δ = 446944.444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-\sqrt{446944.444}}{2*1}=\frac{-50-\sqrt{446944.444}}{2}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+\sqrt{446944.444}}{2*1}=\frac{-50+\sqrt{446944.444}}{2}
$