2n-5/6n=-1

Solution for 2n-5/6n=-1 equation:

2n-5/6n=-1

We move all terms to the left:

2n-5/6n-(-1)=0


Domain of the equation: 6n!=0

n!=0/6

n!=0

n∈R


We add all the numbers together, and all the variables

2n-5/6n+1=0

We multiply all the terms by the denominator


2n*6n+1*6n-5=0

Wy multiply elements

12n^2+6n-5=0

a = 12; b = 6; c = -5;
Δ = b2-4ac
Δ = 62-4·12·(-5)
Δ = 276
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:

$\sqrt{\Delta}=\sqrt{276}=\sqrt{4*69}=\sqrt{4}*\sqrt{69}=2\sqrt{69}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{69}}{2*12}=\frac{-6-2\sqrt{69}}{24}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{69}}{2*12}=\frac{-6+2\sqrt{69}}{24}
$