3y2-2=340

Solution for 3y2-2=340 equation:

3y^2-2=340

We move all terms to the left:

3y^2-2-(340)=0

We add all the numbers together, and all the variables

3y^2-342=0

a = 3; b = 0; c = -342;
Δ = b2-4ac
Δ = 02-4·3·(-342)
Δ = 4104
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:

$\sqrt{\Delta}=\sqrt{4104}=\sqrt{36*114}=\sqrt{36}*\sqrt{114}=6\sqrt{114}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{114}}{2*3}=\frac{0-6\sqrt{114}}{6}
=-\frac{6\sqrt{114}}{6}
=-\sqrt{114}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{114}}{2*3}=\frac{0+6\sqrt{114}}{6}
=\frac{6\sqrt{114}}{6}
=\sqrt{114}
$