5y^2-32=-12y

Solution for 5y^2-32=-12y equation:

5y^2-32=-12y

We move all terms to the left:

5y^2-32-(-12y)=0

We get rid of parentheses

5y^2+12y-32=0

a = 5; b = 12; c = -32;
Δ = b2-4ac
Δ = 122-4·5·(-32)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-28}{2*5}=\frac{-40}{10}
=-4
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+28}{2*5}=\frac{16}{10}
=1+3/5
$