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

Solution for 3y(5y+2)+(-5y-2)=0 equation:

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

We multiply parentheses

15y^2+6y+(-5y-2)=0

We get rid of parentheses

15y^2+6y-5y-2=0

We add all the numbers together, and all the variables

15y^2+y-2=0

a = 15; b = 1; c = -2;
Δ = b2-4ac
Δ = 12-4·15·(-2)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-11}{2*15}=\frac{-12}{30}
=-2/5
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+11}{2*15}=\frac{10}{30}
=1/3
$