7/8n-3/4n-9=2

Solution for 7/8n-3/4n-9=2 equation:

7/8n-3/4n-9=2

We move all terms to the left:

7/8n-3/4n-9-(2)=0


Domain of the equation: 8n!=0

n!=0/8

n!=0

n∈R



Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R


We add all the numbers together, and all the variables

7/8n-3/4n-11=0

We calculate fractions


28n/32n^2+(-24n)/32n^2-11=0

We multiply all the terms by the denominator


28n+(-24n)-11*32n^2=0

Wy multiply elements

-352n^2+28n+(-24n)=0

We get rid of parentheses

-352n^2+28n-24n=0

We add all the numbers together, and all the variables

-352n^2+4n=0

a = -352; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-352)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*-352}=\frac{-8}{-704}
=1/88
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-352}=\frac{0}{-704}
=0
$