0=600x^2-300x-200

Solution for 0=600x^2-300x-200 equation:

0=600x^2-300x-200

We move all terms to the left:

0-(600x^2-300x-200)=0

We add all the numbers together, and all the variables

-(600x^2-300x-200)=0

We get rid of parentheses

-600x^2+300x+200=0

a = -600; b = 300; c = +200;
Δ = b2-4ac
Δ = 3002-4·(-600)·200
Δ = 570000
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:

$\sqrt{\Delta}=\sqrt{570000}=\sqrt{10000*57}=\sqrt{10000}*\sqrt{57}=100\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(300)-100\sqrt{57}}{2*-600}=\frac{-300-100\sqrt{57}}{-1200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(300)+100\sqrt{57}}{2*-600}=\frac{-300+100\sqrt{57}}{-1200}
$