27y2=6y+16

Solution for 27y2=6y+16 equation:

27y^2=6y+16

We move all terms to the left:

27y^2-(6y+16)=0

We get rid of parentheses

27y^2-6y-16=0

a = 27; b = -6; c = -16;
Δ = b2-4ac
Δ = -62-4·27·(-16)
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-42}{2*27}=\frac{-36}{54}
=-2/3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+42}{2*27}=\frac{48}{54}
=8/9
$