7/3n+18/5n=712/75

Solution for 7/3n+18/5n=712/75 equation:

7/3n+18/5n=712/75

We move all terms to the left:

7/3n+18/5n-(712/75)=0


Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R



Domain of the equation: 5n!=0

n!=0/5

n!=0

n∈R


We add all the numbers together, and all the variables

7/3n+18/5n-(+712/75)=0

We get rid of parentheses

7/3n+18/5n-712/75=0

We calculate fractions


(-53400n^2)/7875n^2+18375n/7875n^2+28350n/7875n^2=0

We multiply all the terms by the denominator


(-53400n^2)+18375n+28350n=0

We add all the numbers together, and all the variables

(-53400n^2)+46725n=0

We get rid of parentheses

-53400n^2+46725n=0

a = -53400; b = 46725; c = 0;
Δ = b2-4ac
Δ = 467252-4·(-53400)·0
Δ = 2183225625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2183225625}=46725$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(46725)-46725}{2*-53400}=\frac{-93450}{-106800}
=7/8
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46725)+46725}{2*-53400}=\frac{0}{-106800}
=0
$