1/2n-7=n

Solution for 1/2n-7=n equation:

1/2n-7=n

We move all terms to the left:

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


Domain of the equation: 2n!=0

n!=0/2

n!=0

n∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

a = -2; b = -14; c = +1;
Δ = b2-4ac
Δ = -142-4·(-2)·1
Δ = 204
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:

$\sqrt{\Delta}=\sqrt{204}=\sqrt{4*51}=\sqrt{4}*\sqrt{51}=2\sqrt{51}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{51}}{2*-2}=\frac{14-2\sqrt{51}}{-4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{51}}{2*-2}=\frac{14+2\sqrt{51}}{-4}
$