3y^2+2y=184

Solution for 3y^2+2y=184 equation:

3y^2+2y=184

We move all terms to the left:

3y^2+2y-(184)=0

a = 3; b = 2; c = -184;
Δ = b2-4ac
Δ = 22-4·3·(-184)
Δ = 2212
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:

$\sqrt{\Delta}=\sqrt{2212}=\sqrt{4*553}=\sqrt{4}*\sqrt{553}=2\sqrt{553}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{553}}{2*3}=\frac{-2-2\sqrt{553}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{553}}{2*3}=\frac{-2+2\sqrt{553}}{6}
$