(1/2)n+3=47n+3

Solution for (1/2)n+3=47n+3 equation:

(1/2)n+3=47n+3

We move all terms to the left:

(1/2)n+3-(47n+3)=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-(47n+3)+3=0

We multiply parentheses

n^2-(47n+3)+3=0

We get rid of parentheses

n^2-47n-3+3=0

We add all the numbers together, and all the variables

n^2-47n=0

a = 1; b = -47; c = 0;
Δ = b2-4ac
Δ = -472-4·1·0
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-47)-47}{2*1}=\frac{0}{2}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47)+47}{2*1}=\frac{94}{2}
=47
$