(1/2)n-9=14n/2-9=14

Solution for (1/2)n-9=14n/2-9=14 equation:

(1/2)n-9=14n/2-9=14

We move all terms to the left:

(1/2)n-9-(14n/2-9)=0


Domain of the equation: 2)n!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

(+1/2)n-(14n/2-9)-9=0

We multiply parentheses

n^2-(14n/2-9)-9=0

We get rid of parentheses

n^2-14n/2+9-9=0

We multiply all the terms by the denominator


n^2*2-14n+9*2-9*2=0

We add all the numbers together, and all the variables

n^2*2-14n=0

Wy multiply elements

2n^2-14n=0

a = 2; b = -14; c = 0;
Δ = b2-4ac
Δ = -142-4·2·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-14}{2*2}=\frac{0}{4}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14}{2*2}=\frac{28}{4}
=7
$