(x+8)*x=1000

Solution for (x+8)*x=1000 equation:

(x+8)*x=1000

We move all terms to the left:

(x+8)*x-(1000)=0

We multiply parentheses

x^2+8x-1000=0

a = 1; b = 8; c = -1000;
Δ = b2-4ac
Δ = 82-4·1·(-1000)
Δ = 4064
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:

$\sqrt{\Delta}=\sqrt{4064}=\sqrt{16*254}=\sqrt{16}*\sqrt{254}=4\sqrt{254}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{254}}{2*1}=\frac{-8-4\sqrt{254}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{254}}{2*1}=\frac{-8+4\sqrt{254}}{2}
$