100x=(3250+8x+0.1x^2)

Solution for 100x=(3250+8x+0.1x^2) equation:

100x=(3250+8x+0.1x^2)

We move all terms to the left:

100x-((3250+8x+0.1x^2))=0


We calculate terms in parentheses: -((3250+8x+0.1x^2)), so:

(3250+8x+0.1x^2)

We get rid of parentheses

0.1x^2+8x+3250

Back to the equation:

-(0.1x^2+8x+3250)


We add all the numbers together, and all the variables

100x-(0.1x^2+8x+3250)=0

We get rid of parentheses

-0.1x^2+100x-8x-3250=0

We add all the numbers together, and all the variables

-0.1x^2+92x-3250=0

a = -0.1; b = 92; c = -3250;
Δ = b2-4ac
Δ = 922-4·(-0.1)·(-3250)
Δ = 7164
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:

$\sqrt{\Delta}=\sqrt{7164}=\sqrt{36*199}=\sqrt{36}*\sqrt{199}=6\sqrt{199}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(92)-6\sqrt{199}}{2*-0.1}=\frac{-92-6\sqrt{199}}{-0.2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(92)+6\sqrt{199}}{2*-0.1}=\frac{-92+6\sqrt{199}}{-0.2}
$