6.n=174/n=29

Solution for 6.n=174/n=29 equation:

6.n=174/n=29

We move all terms to the left:

6.n-(174/n)=0


Domain of the equation: n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

6.n-(+174/n)=0

We get rid of parentheses

6.n-174/n=0

We multiply all the terms by the denominator


(6.n)*n-174=0

We add all the numbers together, and all the variables

(+6.n)*n-174=0

We multiply parentheses

6n^2-174=0

a = 6; b = 0; c = -174;
Δ = b2-4ac
Δ = 02-4·6·(-174)
Δ = 4176
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:

$\sqrt{\Delta}=\sqrt{4176}=\sqrt{144*29}=\sqrt{144}*\sqrt{29}=12\sqrt{29}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{29}}{2*6}=\frac{0-12\sqrt{29}}{12}
=-\frac{12\sqrt{29}}{12}
=-\sqrt{29}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{29}}{2*6}=\frac{0+12\sqrt{29}}{12}
=\frac{12\sqrt{29}}{12}
=\sqrt{29}
$