2000x(x-0.03)=6000

Solution for 2000x(x-0.03)=6000 equation:

2000x(x-0.03)=6000

We move all terms to the left:

2000x(x-0.03)-(6000)=0

We multiply parentheses

2000x^2-60x-6000=0

a = 2000; b = -60; c = -6000;
Δ = b2-4ac
Δ = -602-4·2000·(-6000)
Δ = 48003600
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:

$\sqrt{\Delta}=\sqrt{48003600}=\sqrt{400*120009}=\sqrt{400}*\sqrt{120009}=20\sqrt{120009}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-20\sqrt{120009}}{2*2000}=\frac{60-20\sqrt{120009}}{4000}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+20\sqrt{120009}}{2*2000}=\frac{60+20\sqrt{120009}}{4000}
$