-4/3n+1/2n=25/12

Solution for -4/3n+1/2n=25/12 equation:

-4/3n+1/2n=25/12

We move all terms to the left:

-4/3n+1/2n-(25/12)=0


Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R



Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R


We add all the numbers together, and all the variables

-4/3n+1/2n-(+25/12)=0

We get rid of parentheses

-4/3n+1/2n-25/12=0

We calculate fractions


(-300n^2)/72n^2+(-96n)/72n^2+36n/72n^2=0

We multiply all the terms by the denominator


(-300n^2)+(-96n)+36n=0

We add all the numbers together, and all the variables

(-300n^2)+36n+(-96n)=0

We get rid of parentheses

-300n^2+36n-96n=0

We add all the numbers together, and all the variables

-300n^2-60n=0

a = -300; b = -60; c = 0;
Δ = b2-4ac
Δ = -602-4·(-300)·0
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-60}{2*-300}=\frac{0}{-600}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+60}{2*-300}=\frac{120}{-600}
=-1/5
$