(14/5)n=3/5

Solution for (14/5)n=3/5 equation:

(14/5)n=3/5

We move all terms to the left:

(14/5)n-(3/5)=0


Domain of the equation: 5)n!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

(+14/5)n-(+3/5)=0

We multiply parentheses

14n^2-(+3/5)=0

We get rid of parentheses

14n^2-3/5=0

We multiply all the terms by the denominator


14n^2*5-3=0

Wy multiply elements

70n^2-3=0

a = 70; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·70·(-3)
Δ = 840
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:

$\sqrt{\Delta}=\sqrt{840}=\sqrt{4*210}=\sqrt{4}*\sqrt{210}=2\sqrt{210}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{210}}{2*70}=\frac{0-2\sqrt{210}}{140}
=-\frac{2\sqrt{210}}{140}
=-\frac{\sqrt{210}}{70}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{210}}{2*70}=\frac{0+2\sqrt{210}}{140}
=\frac{2\sqrt{210}}{140}
=\frac{\sqrt{210}}{70}
$