6y^2=7

Solution for 6y^2=7 equation:

6y^2=7

We move all terms to the left:

6y^2-(7)=0

a = 6; b = 0; c = -7;
Δ = b2-4ac
Δ = 02-4·6·(-7)
Δ = 168
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{168}=\sqrt{4*42}=\sqrt{4}*\sqrt{42}=2\sqrt{42}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{42}}{2*6}=\frac{0-2\sqrt{42}}{12}
=-\frac{2\sqrt{42}}{12}
=-\frac{\sqrt{42}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{42}}{2*6}=\frac{0+2\sqrt{42}}{12}
=\frac{2\sqrt{42}}{12}
=\frac{\sqrt{42}}{6}
$