6q^2=100

Solution for 6q^2=100 equation:

6q^2=100

We move all terms to the left:

6q^2-(100)=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:
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2400}=\sqrt{400*6}=\sqrt{400}*\sqrt{6}=20\sqrt{6}$
$q_{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}
$
$q_{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}
$