5y(3y+2)=6y+4

Solution for 5y(3y+2)=6y+4 equation:

5y(3y+2)=6y+4

We move all terms to the left:

5y(3y+2)-(6y+4)=0

We multiply parentheses

15y^2+10y-(6y+4)=0

We get rid of parentheses

15y^2+10y-6y-4=0

We add all the numbers together, and all the variables

15y^2+4y-4=0

a = 15; b = 4; c = -4;
Δ = b2-4ac
Δ = 42-4·15·(-4)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-16}{2*15}=\frac{-20}{30}
=-2/3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+16}{2*15}=\frac{12}{30}
=2/5
$