x(10+x)=600

Solution for x(10+x)=600 equation:

x(10+x)=600

We move all terms to the left:

x(10+x)-(600)=0

We add all the numbers together, and all the variables

x(x+10)-600=0

We multiply parentheses

x^2+10x-600=0

a = 1; b = 10; c = -600;
Δ = b2-4ac
Δ = 102-4·1·(-600)
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-50}{2*1}=\frac{-60}{2}
=-30
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+50}{2*1}=\frac{40}{2}
=20
$