3/4n-8=2/3n+5

Solution for 3/4n-8=2/3n+5 equation:

3/4n-8=2/3n+5

We move all terms to the left:

3/4n-8-(2/3n+5)=0


Domain of the equation: 4n!=0

n!=0/4

n!=0

n∈R



Domain of the equation: 3n+5)!=0

n∈R


We get rid of parentheses

3/4n-2/3n-5-8=0

We calculate fractions


9n/12n^2+(-8n)/12n^2-5-8=0

We add all the numbers together, and all the variables

9n/12n^2+(-8n)/12n^2-13=0

We multiply all the terms by the denominator


9n+(-8n)-13*12n^2=0

Wy multiply elements

-156n^2+9n+(-8n)=0

We get rid of parentheses

-156n^2+9n-8n=0

We add all the numbers together, and all the variables

-156n^2+n=0

a = -156; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-156)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-156}=\frac{-2}{-312}
=1/156
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-156}=\frac{0}{-312}
=0
$