110x-(3200+8x+0.1x^2)=0

Solution for 110x-(3200+8x+0.1x^2)=0 equation:

110x-(3200+8x+0.1x^2)=0

We get rid of parentheses

-0.1x^2-8x+110x-3200=0

We add all the numbers together, and all the variables

-0.1x^2+102x-3200=0

a = -0.1; b = 102; c = -3200;
Δ = b2-4ac
Δ = 1022-4·(-0.1)·(-3200)
Δ = 9124
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:

$\sqrt{\Delta}=\sqrt{9124}=\sqrt{4*2281}=\sqrt{4}*\sqrt{2281}=2\sqrt{2281}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(102)-2\sqrt{2281}}{2*-0.1}=\frac{-102-2\sqrt{2281}}{-0.2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(102)+2\sqrt{2281}}{2*-0.1}=\frac{-102+2\sqrt{2281}}{-0.2}
$