7/8n-3/4n=-6

Solution for 7/8n-3/4n=-6 equation:

7/8n-3/4n=-6

We move all terms to the left:

7/8n-3/4n-(-6)=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+6=0

We calculate fractions


28n/32n^2+(-24n)/32n^2+6=0

We multiply all the terms by the denominator


28n+(-24n)+6*32n^2=0

Wy multiply elements

192n^2+28n+(-24n)=0

We get rid of parentheses

192n^2+28n-24n=0

We add all the numbers together, and all the variables

192n^2+4n=0

a = 192; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·192·0
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*192}=\frac{-8}{384}
=-1/48
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*192}=\frac{0}{384}
=0
$