80(x)+x^2=91.1

Solution for 80(x)+x^2=91.1 equation:

80(x)+x^2=91.1

We move all terms to the left:

80(x)+x^2-(91.1)=0

We add all the numbers together, and all the variables

x^2+80x-91.1=0

a = 1; b = 80; c = -91.1;
Δ = b2-4ac
Δ = 802-4·1·(-91.1)
Δ = 6764.4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-\sqrt{6764.4}}{2*1}=\frac{-80-\sqrt{6764.4}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+\sqrt{6764.4}}{2*1}=\frac{-80+\sqrt{6764.4}}{2}
$