100=6x^2

Solution for 100=6x^2 equation:

100=6x^2

We move all terms to the left:

100-(6x^2)=0

a = -6; b = 0; c = +100;
Δ = b2-4ac
Δ = 02-4·(-6)·100
Δ = 2400
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:

$\sqrt{\Delta}=\sqrt{2400}=\sqrt{400*6}=\sqrt{400}*\sqrt{6}=20\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{6}}{2*-6}=\frac{0-20\sqrt{6}}{-12}
=-\frac{20\sqrt{6}}{-12}
=-\frac{5\sqrt{6}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{6}}{2*-6}=\frac{0+20\sqrt{6}}{-12}
=\frac{20\sqrt{6}}{-12}
=\frac{5\sqrt{6}}{-3}
$