15y(y+2)=7y-4

Solution for 15y(y+2)=7y-4 equation:

15y(y+2)=7y-4

We move all terms to the left:

15y(y+2)-(7y-4)=0

We multiply parentheses

15y^2+30y-(7y-4)=0

We get rid of parentheses

15y^2+30y-7y+4=0

We add all the numbers together, and all the variables

15y^2+23y+4=0

a = 15; b = 23; c = +4;
Δ = b2-4ac
Δ = 232-4·15·4
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-17}{2*15}=\frac{-40}{30}
=-1+1/3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+17}{2*15}=\frac{-6}{30}
=-1/5
$