1/2n+7=n+14*2

Solution for 1/2n+7=n+14*2 equation:

1/2n+7=n+14*2

We move all terms to the left:

1/2n+7-(n+14*2)=0


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R


We add all the numbers together, and all the variables

1/2n-(n+28)+7=0

We get rid of parentheses

1/2n-n-28+7=0

We multiply all the terms by the denominator


-n*2n-28*2n+7*2n+1=0

Wy multiply elements

-2n^2-56n+14n+1=0

We add all the numbers together, and all the variables

-2n^2-42n+1=0

a = -2; b = -42; c = +1;
Δ = b2-4ac
Δ = -422-4·(-2)·1
Δ = 1772
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:

$\sqrt{\Delta}=\sqrt{1772}=\sqrt{4*443}=\sqrt{4}*\sqrt{443}=2\sqrt{443}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{443}}{2*-2}=\frac{42-2\sqrt{443}}{-4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{443}}{2*-2}=\frac{42+2\sqrt{443}}{-4}
$