0.1x^2-x=1000

Solution for 0.1x^2-x=1000 equation:

0.1x^2-x=1000

We move all terms to the left:

0.1x^2-x-(1000)=0

We add all the numbers together, and all the variables

0.1x^2-1x-1000=0

a = 0.1; b = -1; c = -1000;
Δ = b2-4ac
Δ = -12-4·0.1·(-1000)
Δ = 401
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{-(-1)-\sqrt{401}}{2*0.1}=\frac{1-\sqrt{401}}{0.2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{401}}{2*0.1}=\frac{1+\sqrt{401}}{0.2}
$