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*7!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-14n^2*7-98n*7+1=0

Wy multiply elements

-98n^2-686n+1=0

a = -98; b = -686; c = +1;
Δ = b2-4ac
Δ = -6862-4·(-98)·1
Δ = 470988
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:

$\sqrt{\Delta}=\sqrt{470988}=\sqrt{1764*267}=\sqrt{1764}*\sqrt{267}=42\sqrt{267}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-686)-42\sqrt{267}}{2*-98}=\frac{686-42\sqrt{267}}{-196}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-686)+42\sqrt{267}}{2*-98}=\frac{686+42\sqrt{267}}{-196}
$