6x^2=1000

Solution for 6x^2=1000 equation:

6x^2=1000

We move all terms to the left:

6x^2-(1000)=0

a = 6; b = 0; c = -1000;
Δ = b2-4ac
Δ = 02-4·6·(-1000)
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*6}=\frac{0-40\sqrt{15}}{12}
=-\frac{40\sqrt{15}}{12}
=-\frac{10\sqrt{15}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{15}}{2*6}=\frac{0+40\sqrt{15}}{12}
=\frac{40\sqrt{15}}{12}
=\frac{10\sqrt{15}}{3}
$