49n-8-1/3n=7

Solution for 49n-8-1/3n=7 equation:

49n-8-1/3n=7

We move all terms to the left:

49n-8-1/3n-(7)=0


Domain of the equation: 3n!=0

n!=0/3

n!=0

n∈R


We add all the numbers together, and all the variables

49n-1/3n-15=0

We multiply all the terms by the denominator


49n*3n-15*3n-1=0

Wy multiply elements

147n^2-45n-1=0

a = 147; b = -45; c = -1;
Δ = b2-4ac
Δ = -452-4·147·(-1)
Δ = 2613
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-\sqrt{2613}}{2*147}=\frac{45-\sqrt{2613}}{294}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{2613}}{2*147}=\frac{45+\sqrt{2613}}{294}
$