100x=3200+9x+0.1x^2

Solution for 100x=3200+9x+0.1x^2 equation:

100x=3200+9x+0.1x^2

We move all terms to the left:

100x-(3200+9x+0.1x^2)=0

We get rid of parentheses

-0.1x^2-9x+100x-3200=0

We add all the numbers together, and all the variables

-0.1x^2+91x-3200=0

a = -0.1; b = 91; c = -3200;
Δ = b2-4ac
Δ = 912-4·(-0.1)·(-3200)
Δ = 7001
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{-(91)-\sqrt{7001}}{2*-0.1}=\frac{-91-\sqrt{7001}}{-0.2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(91)+\sqrt{7001}}{2*-0.1}=\frac{-91+\sqrt{7001}}{-0.2}
$