1000=2x^2+x

Solution for 1000=2x^2+x equation:

1000=2x^2+x

We move all terms to the left:

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

We get rid of parentheses

-2x^2-x+1000=0

We add all the numbers together, and all the variables

-2x^2-1x+1000=0

a = -2; b = -1; c = +1000;
Δ = b2-4ac
Δ = -12-4·(-2)·1000
Δ = 8001
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:

$\sqrt{\Delta}=\sqrt{8001}=\sqrt{9*889}=\sqrt{9}*\sqrt{889}=3\sqrt{889}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-3\sqrt{889}}{2*-2}=\frac{1-3\sqrt{889}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+3\sqrt{889}}{2*-2}=\frac{1+3\sqrt{889}}{-4}
$