2x^2=3000

Solution for 2x^2=3000 equation:

2x^2=3000

We move all terms to the left:

2x^2-(3000)=0

a = 2; b = 0; c = -3000;
Δ = b2-4ac
Δ = 02-4·2·(-3000)
Δ = 24000
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:

$\sqrt{\Delta}=\sqrt{24000}=\sqrt{1600*15}=\sqrt{1600}*\sqrt{15}=40\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{15}}{2*2}=\frac{0-40\sqrt{15}}{4}
=-\frac{40\sqrt{15}}{4}
=-10\sqrt{15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{15}}{2*2}=\frac{0+40\sqrt{15}}{4}
=\frac{40\sqrt{15}}{4}
=10\sqrt{15}
$