-8y=3y^2+5

Solution for -8y=3y^2+5 equation:

-8y=3y^2+5

We move all terms to the left:

-8y-(3y^2+5)=0

We get rid of parentheses

-3y^2-8y-5=0

a = -3; b = -8; c = -5;
Δ = b2-4ac
Δ = -82-4·(-3)·(-5)
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2}{2*-3}=\frac{6}{-6}
=-1
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2}{2*-3}=\frac{10}{-6}
=-1+2/3
$