7/6-4/3n=1/2n+3

Solution for 7/6-4/3n=1/2n+3 equation:

7/6-4/3n=1/2n+3

We move all terms to the left:

7/6-4/3n-(1/2n+3)=0


Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R



Domain of the equation: 2n+3)!=0

n∈R


We get rid of parentheses

-4/3n-1/2n-3+7/6=0

We calculate fractions


84n^2/216n^2+(-288n)/216n^2+(-108n)/216n^2-3=0

We multiply all the terms by the denominator


84n^2+(-288n)+(-108n)-3*216n^2=0

Wy multiply elements

84n^2-648n^2+(-288n)+(-108n)=0

We get rid of parentheses

84n^2-648n^2-288n-108n=0

We add all the numbers together, and all the variables

-564n^2-396n=0

a = -564; b = -396; c = 0;
Δ = b2-4ac
Δ = -3962-4·(-564)·0
Δ = 156816
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{156816}=396$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-396)-396}{2*-564}=\frac{0}{-1128}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-396)+396}{2*-564}=\frac{792}{-1128}
=-33/47
$