3y2=-4y+16

Solution for 3y2=-4y+16 equation:

3y^2=-4y+16

We move all terms to the left:

3y^2-(-4y+16)=0

We get rid of parentheses

3y^2+4y-16=0

a = 3; b = 4; c = -16;
Δ = b2-4ac
Δ = 42-4·3·(-16)
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{13}}{2*3}=\frac{-4-4\sqrt{13}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{13}}{2*3}=\frac{-4+4\sqrt{13}}{6}
$