6+m=1/3m-8

Solution for 6+m=1/3m-8 equation:

6+m=1/3m-8

We move all terms to the left:

6+m-(1/3m-8)=0


Domain of the equation: 3m-8)!=0

m∈R


We get rid of parentheses

m-1/3m+8+6=0

We multiply all the terms by the denominator


m*3m+8*3m+6*3m-1=0

Wy multiply elements

3m^2+24m+18m-1=0

We add all the numbers together, and all the variables

3m^2+42m-1=0

a = 3; b = 42; c = -1;
Δ = b2-4ac
Δ = 422-4·3·(-1)
Δ = 1776
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1776}=\sqrt{16*111}=\sqrt{16}*\sqrt{111}=4\sqrt{111}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-4\sqrt{111}}{2*3}=\frac{-42-4\sqrt{111}}{6}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+4\sqrt{111}}{2*3}=\frac{-42+4\sqrt{111}}{6}
$