4/9n-8-1/7n=7

Solution for 4/9n-8-1/7n=7 equation:

4/9n-8-1/7n=7

We move all terms to the left:

4/9n-8-1/7n-(7)=0


Domain of the equation: 9n!=0

n!=0/9

n!=0

n∈R



Domain of the equation: 7n!=0

n!=0/7

n!=0

n∈R


We add all the numbers together, and all the variables

4/9n-1/7n-15=0

We calculate fractions


28n/63n^2+(-9n)/63n^2-15=0

We multiply all the terms by the denominator


28n+(-9n)-15*63n^2=0

Wy multiply elements

-945n^2+28n+(-9n)=0

We get rid of parentheses

-945n^2+28n-9n=0

We add all the numbers together, and all the variables

-945n^2+19n=0

a = -945; b = 19; c = 0;
Δ = b2-4ac
Δ = 192-4·(-945)·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-19}{2*-945}=\frac{-38}{-1890}
=19/945
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+19}{2*-945}=\frac{0}{-1890}
=0
$