4n+11=6/8n+-4.5

Solution for 4n+11=6/8n+-4.5 equation:

4n+11=6/8n+-4.5

We move all terms to the left:

4n+11-(6/8n+-4.5)=0


Domain of the equation: 8n+-4.5)!=0

n∈R


We add all the numbers together, and all the variables

4n-(6/8n-4.5)+11=0

We get rid of parentheses

4n-6/8n+4.5+11=0

We multiply all the terms by the denominator


4n*8n+(4.5)*8n+11*8n-6=0

We multiply parentheses

4n*8n+36n+11*8n-6=0

Wy multiply elements

32n^2+36n+88n-6=0

We add all the numbers together, and all the variables

32n^2+124n-6=0

a = 32; b = 124; c = -6;
Δ = b2-4ac
Δ = 1242-4·32·(-6)
Δ = 16144
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:

$\sqrt{\Delta}=\sqrt{16144}=\sqrt{16*1009}=\sqrt{16}*\sqrt{1009}=4\sqrt{1009}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(124)-4\sqrt{1009}}{2*32}=\frac{-124-4\sqrt{1009}}{64}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(124)+4\sqrt{1009}}{2*32}=\frac{-124+4\sqrt{1009}}{64}
$