15n(n+2)=7n+4

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

15n(n+2)=7n+4

We move all terms to the left:

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

We multiply parentheses

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

15n^2+23n-4=0

a = 15; b = 23; c = -4;
Δ = b2-4ac
Δ = 232-4·15·(-4)
Δ = 769
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-\sqrt{769}}{2*15}=\frac{-23-\sqrt{769}}{30}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+\sqrt{769}}{2*15}=\frac{-23+\sqrt{769}}{30}
$