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

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

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

We move all terms to the left:

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


Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R



Domain of the equation: 8n+7)!=0

n∈R


We get rid of parentheses

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

We calculate fractions


24n/32n^2+(-28n)/32n^2-7+2=0

We add all the numbers together, and all the variables

24n/32n^2+(-28n)/32n^2-5=0

We multiply all the terms by the denominator


24n+(-28n)-5*32n^2=0

Wy multiply elements

-160n^2+24n+(-28n)=0

We get rid of parentheses

-160n^2+24n-28n=0

We add all the numbers together, and all the variables

-160n^2-4n=0

a = -160; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-160)·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*-160}=\frac{0}{-320}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-160}=\frac{8}{-320}
=-1/40
$