3000=6x^2

Solution for 3000=6x^2 equation:

3000=6x^2

We move all terms to the left:

3000-(6x^2)=0

a = -6; b = 0; c = +3000;
Δ = b2-4ac
Δ = 02-4·(-6)·3000
Δ = 72000
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:

$\sqrt{\Delta}=\sqrt{72000}=\sqrt{14400*5}=\sqrt{14400}*\sqrt{5}=120\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-120\sqrt{5}}{2*-6}=\frac{0-120\sqrt{5}}{-12}
=-\frac{120\sqrt{5}}{-12}
=-\frac{10\sqrt{5}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+120\sqrt{5}}{2*-6}=\frac{0+120\sqrt{5}}{-12}
=\frac{120\sqrt{5}}{-12}
=\frac{10\sqrt{5}}{-1}
$