x(x-10)=3000

Solution for x(x-10)=3000 equation:

x(x-10)=3000

We move all terms to the left:

x(x-10)-(3000)=0

We multiply parentheses

x^2-10x-3000=0

a = 1; b = -10; c = -3000;
Δ = b2-4ac
Δ = -102-4·1·(-3000)
Δ = 12100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12100}=110$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-110}{2*1}=\frac{-100}{2}
=-50
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+110}{2*1}=\frac{120}{2}
=60
$