x^2+8x=600

Solution for x^2+8x=600 equation:

x^2+8x=600

We move all terms to the left:

x^2+8x-(600)=0

a = 1; b = 8; c = -600;
Δ = b2-4ac
Δ = 82-4·1·(-600)
Δ = 2464
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:

$\sqrt{\Delta}=\sqrt{2464}=\sqrt{16*154}=\sqrt{16}*\sqrt{154}=4\sqrt{154}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{154}}{2*1}=\frac{-8-4\sqrt{154}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{154}}{2*1}=\frac{-8+4\sqrt{154}}{2}
$