m+1/3m+21+m+8=71

Solution for m+1/3m+21+m+8=71 equation:

m+1/3m+21+m+8=71

We move all terms to the left:

m+1/3m+21+m+8-(71)=0


Domain of the equation: 3m!=0

m!=0/3

m!=0

m∈R


We add all the numbers together, and all the variables

2m+1/3m-42=0

We multiply all the terms by the denominator


2m*3m-42*3m+1=0

Wy multiply elements

6m^2-126m+1=0

a = 6; b = -126; c = +1;
Δ = b2-4ac
Δ = -1262-4·6·1
Δ = 15852
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:

$\sqrt{\Delta}=\sqrt{15852}=\sqrt{4*3963}=\sqrt{4}*\sqrt{3963}=2\sqrt{3963}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-126)-2\sqrt{3963}}{2*6}=\frac{126-2\sqrt{3963}}{12}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-126)+2\sqrt{3963}}{2*6}=\frac{126+2\sqrt{3963}}{12}
$