(21/10)n=11/6

Solution for (21/10)n=11/6 equation:

(21/10)n=11/6

We move all terms to the left:

(21/10)n-(11/6)=0


Domain of the equation: 10)n!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

(+21/10)n-(+11/6)=0

We multiply parentheses

21n^2-(+11/6)=0

We get rid of parentheses

21n^2-11/6=0

We multiply all the terms by the denominator


21n^2*6-11=0

Wy multiply elements

126n^2-11=0

a = 126; b = 0; c = -11;
Δ = b2-4ac
Δ = 02-4·126·(-11)
Δ = 5544
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:

$\sqrt{\Delta}=\sqrt{5544}=\sqrt{36*154}=\sqrt{36}*\sqrt{154}=6\sqrt{154}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{154}}{2*126}=\frac{0-6\sqrt{154}}{252}
=-\frac{6\sqrt{154}}{252}
=-\frac{\sqrt{154}}{42}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{154}}{2*126}=\frac{0+6\sqrt{154}}{252}
=\frac{6\sqrt{154}}{252}
=\frac{\sqrt{154}}{42}
$