6y^2-4y=16

Solution for 6y^2-4y=16 equation:

6y^2-4y=16

We move all terms to the left:

6y^2-4y-(16)=0

a = 6; b = -4; c = -16;
Δ = b2-4ac
Δ = -42-4·6·(-16)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-20}{2*6}=\frac{-16}{12}
=-1+1/3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+20}{2*6}=\frac{24}{12}
=2
$