1000=20x+5x^2

Solution for 1000=20x+5x^2 equation:

1000=20x+5x^2

We move all terms to the left:

1000-(20x+5x^2)=0

We get rid of parentheses

-5x^2-20x+1000=0

a = -5; b = -20; c = +1000;
Δ = b2-4ac
Δ = -202-4·(-5)·1000
Δ = 20400
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:

$\sqrt{\Delta}=\sqrt{20400}=\sqrt{400*51}=\sqrt{400}*\sqrt{51}=20\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20\sqrt{51}}{2*-5}=\frac{20-20\sqrt{51}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20\sqrt{51}}{2*-5}=\frac{20+20\sqrt{51}}{-10}
$