6v2=23

Solution for 6v2=23 equation:

6v^2=23

We move all terms to the left:

6v^2-(23)=0

a = 6; b = 0; c = -23;
Δ = b2-4ac
Δ = 02-4·6·(-23)
Δ = 552
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{552}=\sqrt{4*138}=\sqrt{4}*\sqrt{138}=2\sqrt{138}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{138}}{2*6}=\frac{0-2\sqrt{138}}{12}
=-\frac{2\sqrt{138}}{12}
=-\frac{\sqrt{138}}{6}
$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{138}}{2*6}=\frac{0+2\sqrt{138}}{12}
=\frac{2\sqrt{138}}{12}
=\frac{\sqrt{138}}{6}
$