1000=100x+2x*x

Solution for 1000=100x+2x*x equation:

1000=100x+2x*x

We move all terms to the left:

1000-(100x+2x*x)=0

We add all the numbers together, and all the variables

-(+100x+2x*x)+1000=0

We get rid of parentheses

-100x-2x*x+1000=0

Wy multiply elements

-2x^2-100x+1000=0

a = -2; b = -100; c = +1000;
Δ = b2-4ac
Δ = -1002-4·(-2)·1000
Δ = 18000
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:

$\sqrt{\Delta}=\sqrt{18000}=\sqrt{3600*5}=\sqrt{3600}*\sqrt{5}=60\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-60\sqrt{5}}{2*-2}=\frac{100-60\sqrt{5}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+60\sqrt{5}}{2*-2}=\frac{100+60\sqrt{5}}{-4}
$