6w^2=91

Solution for 6w^2=91 equation:

6w^2=91

We move all terms to the left:

6w^2-(91)=0

a = 6; b = 0; c = -91;
Δ = b2-4ac
Δ = 02-4·6·(-91)
Δ = 2184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2184}=\sqrt{4*546}=\sqrt{4}*\sqrt{546}=2\sqrt{546}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{546}}{2*6}=\frac{0-2\sqrt{546}}{12}
=-\frac{2\sqrt{546}}{12}
=-\frac{\sqrt{546}}{6}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{546}}{2*6}=\frac{0+2\sqrt{546}}{12}
=\frac{2\sqrt{546}}{12}
=\frac{\sqrt{546}}{6}
$