7/6n+1/2n=5

Solution for 7/6n+1/2n=5 equation:

7/6n+1/2n=5

We move all terms to the left:

7/6n+1/2n-(5)=0


Domain of the equation: 6n!=0

n!=0/6

n!=0

n∈R



Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R


We calculate fractions


14n/12n^2+6n/12n^2-5=0

We multiply all the terms by the denominator


14n+6n-5*12n^2=0

We add all the numbers together, and all the variables

20n-5*12n^2=0

Wy multiply elements

-60n^2+20n=0

a = -60; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·(-60)·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20}{2*-60}=\frac{-40}{-120}
=1/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*-60}=\frac{0}{-120}
=0
$