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

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

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

We move all terms to the left:

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


Domain of the equation: 7n!=0

n!=0/7

n!=0

n∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-7n^2-49n+49n+1=0

We add all the numbers together, and all the variables

-7n^2+1=0

a = -7; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-7)·1
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{7}}{2*-7}=\frac{0-2\sqrt{7}}{-14}
=-\frac{2\sqrt{7}}{-14}
=-\frac{\sqrt{7}}{-7}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{7}}{2*-7}=\frac{0+2\sqrt{7}}{-14}
=\frac{2\sqrt{7}}{-14}
=\frac{\sqrt{7}}{-7}
$