3n-5=5/3n+7

Solution for 3n-5=5/3n+7 equation:

3n-5=5/3n+7

We move all terms to the left:

3n-5-(5/3n+7)=0


Domain of the equation: 3n+7)!=0

n∈R


We get rid of parentheses

3n-5/3n-7-5=0

We multiply all the terms by the denominator


3n*3n-7*3n-5*3n-5=0

Wy multiply elements

9n^2-21n-15n-5=0

We add all the numbers together, and all the variables

9n^2-36n-5=0

a = 9; b = -36; c = -5;
Δ = b2-4ac
Δ = -362-4·9·(-5)
Δ = 1476
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1476}=\sqrt{36*41}=\sqrt{36}*\sqrt{41}=6\sqrt{41}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-6\sqrt{41}}{2*9}=\frac{36-6\sqrt{41}}{18}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+6\sqrt{41}}{2*9}=\frac{36+6\sqrt{41}}{18}
$