-16y-5=3y^2

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

-16y-5=3y^2

We move all terms to the left:

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

determiningTheFunctionDomain
-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{2}{-6}
=-1/3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+14}{2*-3}=\frac{30}{-6}
=-5
$