15-1/6n=6n-1

Solution for 15-1/6n=6n-1 equation:

15-1/6n=6n-1

We move all terms to the left:

15-1/6n-(6n-1)=0


Domain of the equation: 6n!=0

n!=0/6

n!=0

n∈R


We get rid of parentheses

-1/6n-6n+1+15=0

We multiply all the terms by the denominator


-6n*6n+1*6n+15*6n-1=0

Wy multiply elements

-36n^2+6n+90n-1=0

We add all the numbers together, and all the variables

-36n^2+96n-1=0

a = -36; b = 96; c = -1;
Δ = b2-4ac
Δ = 962-4·(-36)·(-1)
Δ = 9072
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:

$\sqrt{\Delta}=\sqrt{9072}=\sqrt{1296*7}=\sqrt{1296}*\sqrt{7}=36\sqrt{7}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(96)-36\sqrt{7}}{2*-36}=\frac{-96-36\sqrt{7}}{-72}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(96)+36\sqrt{7}}{2*-36}=\frac{-96+36\sqrt{7}}{-72}
$