7/3n+3=4/5n+15

Solution for 7/3n+3=4/5n+15 equation:

7/3n+3=4/5n+15

We move all terms to the left:

7/3n+3-(4/5n+15)=0


Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R



Domain of the equation: 5n+15)!=0

n∈R


We get rid of parentheses

7/3n-4/5n-15+3=0

We calculate fractions


35n/15n^2+(-12n)/15n^2-15+3=0

We add all the numbers together, and all the variables

35n/15n^2+(-12n)/15n^2-12=0

We multiply all the terms by the denominator


35n+(-12n)-12*15n^2=0

Wy multiply elements

-180n^2+35n+(-12n)=0

We get rid of parentheses

-180n^2+35n-12n=0

We add all the numbers together, and all the variables

-180n^2+23n=0

a = -180; b = 23; c = 0;
Δ = b2-4ac
Δ = 232-4·(-180)·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-23}{2*-180}=\frac{-46}{-360}
=23/180
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+23}{2*-180}=\frac{0}{-360}
=0
$