3y^2+5=-16y

Solution for 3y^2+5=-16y equation:

3y^2+5=-16y

We move all terms to the left:

3y^2+5-(-16y)=0

We get rid of parentheses

3y^2+16y+5=0

a = 3; b = 16; c = +5;
Δ = b2-4ac
Δ = 162-4·3·5
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{-(16)-14}{2*3}=\frac{-30}{6}
=-5
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+14}{2*3}=\frac{-2}{6}
=-1/3
$