x*(x-10)=600

Solution for x*(x-10)=600 equation:

x(x-10)=600

We move all terms to the left:

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