-8y=5y^2-4

Solution for -8y=5y^2-4 equation:

-8y=5y^2-4

We move all terms to the left:

-8y-(5y^2-4)=0

We get rid of parentheses

-5y^2-8y+4=0

a = -5; b = -8; c = +4;
Δ = b2-4ac
Δ = -82-4·(-5)·4
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-12}{2*-5}=\frac{-4}{-10}
=2/5
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+12}{2*-5}=\frac{20}{-10}
=-2
$