8000=500x(1+x)2

Solution for 8000=500x(1+x)2 equation:

8000=500x(1+x)2

We move all terms to the left:

8000-(500x(1+x)2)=0

We add all the numbers together, and all the variables

-(500x(x+1)2)+8000=0


We calculate terms in parentheses: -(500x(x+1)2), so:

500x(x+1)2

We multiply parentheses

1000x^2+1000x

Back to the equation:

-(1000x^2+1000x)


We get rid of parentheses

-1000x^2-1000x+8000=0

a = -1000; b = -1000; c = +8000;
Δ = b2-4ac
Δ = -10002-4·(-1000)·8000
Δ = 33000000
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:

$\sqrt{\Delta}=\sqrt{33000000}=\sqrt{1000000*33}=\sqrt{1000000}*\sqrt{33}=1000\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1000)-1000\sqrt{33}}{2*-1000}=\frac{1000-1000\sqrt{33}}{-2000}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1000)+1000\sqrt{33}}{2*-1000}=\frac{1000+1000\sqrt{33}}{-2000}
$