(1/2)n+6=20

Solution for (1/2)n+6=20 equation:

(1/2)n+6=20

We move all terms to the left:

(1/2)n+6-(20)=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+6-20=0

We add all the numbers together, and all the variables

(+1/2)n-14=0

We multiply parentheses

n^2-14=0

a = 1; b = 0; c = -14;
Δ = b2-4ac
Δ = 02-4·1·(-14)
Δ = 56
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:

$\sqrt{\Delta}=\sqrt{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{14}}{2*1}=\frac{0-2\sqrt{14}}{2}
=-\frac{2\sqrt{14}}{2}
=-\sqrt{14}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{14}}{2*1}=\frac{0+2\sqrt{14}}{2}
=\frac{2\sqrt{14}}{2}
=\sqrt{14}
$