4n+9=1/2(14n)

Solution for 4n+9=1/2(14n) equation:

4n+9=1/2(14n)

We move all terms to the left:

4n+9-(1/2(14n))=0


Domain of the equation: 214n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

4n-(+1/214n)+9=0

We get rid of parentheses

4n-1/214n+9=0

We multiply all the terms by the denominator


4n*214n+9*214n-1=0

Wy multiply elements

856n^2+1926n-1=0

a = 856; b = 1926; c = -1;
Δ = b2-4ac
Δ = 19262-4·856·(-1)
Δ = 3712900
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:

$\sqrt{\Delta}=\sqrt{3712900}=\sqrt{100*37129}=\sqrt{100}*\sqrt{37129}=10\sqrt{37129}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1926)-10\sqrt{37129}}{2*856}=\frac{-1926-10\sqrt{37129}}{1712}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1926)+10\sqrt{37129}}{2*856}=\frac{-1926+10\sqrt{37129}}{1712}
$