3y^2-2y=16

Solution for 3y^2-2y=16 equation:

3y^2-2y=16

We move all terms to the left:

3y^2-2y-(16)=0

a = 3; b = -2; c = -16;
Δ = b2-4ac
Δ = -22-4·3·(-16)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-14}{2*3}=\frac{-12}{6}
=-2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+14}{2*3}=\frac{16}{6}
=2+2/3
$