0=5y^2-8y-32

Solution for 0=5y^2-8y-32 equation:

0=5y^2-8y-32

We move all terms to the left:

0-(5y^2-8y-32)=0

We add all the numbers together, and all the variables

-(5y^2-8y-32)=0

We get rid of parentheses

-5y^2+8y+32=0

a = -5; b = 8; c = +32;
Δ = b2-4ac
Δ = 82-4·(-5)·32
Δ = 704
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:

$\sqrt{\Delta}=\sqrt{704}=\sqrt{64*11}=\sqrt{64}*\sqrt{11}=8\sqrt{11}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8\sqrt{11}}{2*-5}=\frac{-8-8\sqrt{11}}{-10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8\sqrt{11}}{2*-5}=\frac{-8+8\sqrt{11}}{-10}
$