3x^2-320x-6000=200

Solution for 3x^2-320x-6000=200 equation:

3x^2-320x-6000=200

We move all terms to the left:

3x^2-320x-6000-(200)=0

We add all the numbers together, and all the variables

3x^2-320x-6200=0

a = 3; b = -320; c = -6200;
Δ = b2-4ac
Δ = -3202-4·3·(-6200)
Δ = 176800
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:

$\sqrt{\Delta}=\sqrt{176800}=\sqrt{400*442}=\sqrt{400}*\sqrt{442}=20\sqrt{442}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-320)-20\sqrt{442}}{2*3}=\frac{320-20\sqrt{442}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-320)+20\sqrt{442}}{2*3}=\frac{320+20\sqrt{442}}{6}
$