(2/3)n-7=n

Solution for (2/3)n-7=n equation:

(2/3)n-7=n

We move all terms to the left:

(2/3)n-7-(n)=0


Domain of the equation: 3)n!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

(+2/3)n-n-7=0

We add all the numbers together, and all the variables

-1n+(+2/3)n-7=0

We multiply parentheses

2n^2-1n-7=0

a = 2; b = -1; c = -7;
Δ = b2-4ac
Δ = -12-4·2·(-7)
Δ = 57
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{57}}{2*2}=\frac{1-\sqrt{57}}{4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{57}}{2*2}=\frac{1+\sqrt{57}}{4}
$