1/2n+22=6n

Solution for 1/2n+22=6n equation:

1/2n+22=6n

We move all terms to the left:

1/2n+22-(6n)=0


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R


We add all the numbers together, and all the variables

-6n+1/2n+22=0

We multiply all the terms by the denominator


-6n*2n+22*2n+1=0

Wy multiply elements

-12n^2+44n+1=0

a = -12; b = 44; c = +1;
Δ = b2-4ac
Δ = 442-4·(-12)·1
Δ = 1984
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:

$\sqrt{\Delta}=\sqrt{1984}=\sqrt{64*31}=\sqrt{64}*\sqrt{31}=8\sqrt{31}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-8\sqrt{31}}{2*-12}=\frac{-44-8\sqrt{31}}{-24}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+8\sqrt{31}}{2*-12}=\frac{-44+8\sqrt{31}}{-24}
$