x^2+111x+3080.25=104000

Solution for x^2+111x+3080.25=104000 equation:

x^2+111x+3080.25=104000

We move all terms to the left:

x^2+111x+3080.25-(104000)=0

We add all the numbers together, and all the variables

x^2+111x-100919.75=0

a = 1; b = 111; c = -100919.75;
Δ = b2-4ac
Δ = 1112-4·1·(-100919.75)
Δ = 416000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{416000}=\sqrt{6400*65}=\sqrt{6400}*\sqrt{65}=80\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(111)-80\sqrt{65}}{2*1}=\frac{-111-80\sqrt{65}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(111)+80\sqrt{65}}{2*1}=\frac{-111+80\sqrt{65}}{2}
$