1/n+3/4=5/6n-1

Solution for 1/n+3/4=5/6n-1 equation:

1/n+3/4=5/6n-1

We move all terms to the left:

1/n+3/4-(5/6n-1)=0


Domain of the equation: n!=0

n∈R



Domain of the equation: 6n-1)!=0

n∈R


We get rid of parentheses

1/n-5/6n+1+3/4=0

We calculate fractions


108n^2/96n^2+96n/96n^2+(-80n)/96n^2+1=0

We multiply all the terms by the denominator


108n^2+96n+(-80n)+1*96n^2=0

Wy multiply elements

108n^2+96n^2+96n+(-80n)=0

We get rid of parentheses

108n^2+96n^2+96n-80n=0

We add all the numbers together, and all the variables

204n^2+16n=0

a = 204; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·204·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*204}=\frac{-32}{408}
=-4/51
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*204}=\frac{0}{408}
=0
$