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

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

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

We move all terms to the left:

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


Domain of the equation: n!=0

n∈R



Domain of the equation: 3n)!=0

n!=0/1

n!=0

n∈R


We get rid of parentheses

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

We calculate fractions


(-9n^2)/12n^2+48n/12n^2+24n/12n^2=0

We multiply all the terms by the denominator


(-9n^2)+48n+24n=0

We add all the numbers together, and all the variables

(-9n^2)+72n=0

We get rid of parentheses

-9n^2+72n=0

a = -9; b = 72; c = 0;
Δ = b2-4ac
Δ = 722-4·(-9)·0
Δ = 5184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5184}=72$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-72}{2*-9}=\frac{-144}{-18}
=+8
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+72}{2*-9}=\frac{0}{-18}
=0
$