3n+8-6n=n+84-3/8n

Solution for 3n+8-6n=n+84-3/8n equation:

3n+8-6n=n+84-3/8n

We move all terms to the left:

3n+8-6n-(n+84-3/8n)=0


Domain of the equation: 8n)!=0

n!=0/1

n!=0

n∈R


We add all the numbers together, and all the variables

3n-6n-(n-3/8n+84)+8=0

We add all the numbers together, and all the variables

-3n-(n-3/8n+84)+8=0

We get rid of parentheses

-3n-n+3/8n-84+8=0

We multiply all the terms by the denominator


-3n*8n-n*8n-84*8n+8*8n+3=0

Wy multiply elements

-24n^2-8n^2-672n+64n+3=0

We add all the numbers together, and all the variables

-32n^2-608n+3=0

a = -32; b = -608; c = +3;
Δ = b2-4ac
Δ = -6082-4·(-32)·3
Δ = 370048
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:

$\sqrt{\Delta}=\sqrt{370048}=\sqrt{3136*118}=\sqrt{3136}*\sqrt{118}=56\sqrt{118}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-608)-56\sqrt{118}}{2*-32}=\frac{608-56\sqrt{118}}{-64}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-608)+56\sqrt{118}}{2*-32}=\frac{608+56\sqrt{118}}{-64}
$