(5y-8)(3y+1)=0

Solution for (5y-8)(3y+1)=0 equation:

(5y-8)(3y+1)=0

We multiply parentheses ..

(+15y^2+5y-24y-8)=0

We get rid of parentheses

15y^2+5y-24y-8=0

We add all the numbers together, and all the variables

15y^2-19y-8=0

a = 15; b = -19; c = -8;
Δ = b2-4ac
Δ = -192-4·15·(-8)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-29}{2*15}=\frac{-10}{30}
=-1/3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+29}{2*15}=\frac{48}{30}
=1+3/5
$