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

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

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

We move all terms to the left:

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


Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R



Domain of the equation: 8n+4)!=0

n∈R


We get rid of parentheses

3/4n+7/8n-4-2=0

We calculate fractions


24n/32n^2+28n/32n^2-4-2=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

52n-6*32n^2=0

Wy multiply elements

-192n^2+52n=0

a = -192; b = 52; c = 0;
Δ = b2-4ac
Δ = 522-4·(-192)·0
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-52}{2*-192}=\frac{-104}{-384}
=13/48
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+52}{2*-192}=\frac{0}{-384}
=0
$