210=-1000x^2+1100x-2.5

Solution for 210=-1000x^2+1100x-2.5 equation:

210=-1000x^2+1100x-2.5

We move all terms to the left:

210-(-1000x^2+1100x-2.5)=0

We get rid of parentheses

1000x^2-1100x+2.5+210=0

We add all the numbers together, and all the variables

1000x^2-1100x+212.5=0

a = 1000; b = -1100; c = +212.5;
Δ = b2-4ac
Δ = -11002-4·1000·212.5
Δ = 360000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{360000}=600$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1100)-600}{2*1000}=\frac{500}{2000}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1100)+600}{2*1000}=\frac{1700}{2000}
=17/20
$