3y^2=178

Solution for 3y^2=178 equation:

3y^2=178

We move all terms to the left:

3y^2-(178)=0

a = 3; b = 0; c = -178;
Δ = b2-4ac
Δ = 02-4·3·(-178)
Δ = 2136
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:

$\sqrt{\Delta}=\sqrt{2136}=\sqrt{4*534}=\sqrt{4}*\sqrt{534}=2\sqrt{534}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{534}}{2*3}=\frac{0-2\sqrt{534}}{6}
=-\frac{2\sqrt{534}}{6}
=-\frac{\sqrt{534}}{3}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{534}}{2*3}=\frac{0+2\sqrt{534}}{6}
=\frac{2\sqrt{534}}{6}
=\frac{\sqrt{534}}{3}
$