1/m+5/m+1=6m

Solution for 1/m+5/m+1=6m equation:

1/m+5/m+1=6m

We move all terms to the left:

1/m+5/m+1-(6m)=0


Domain of the equation: m!=0

m∈R


We add all the numbers together, and all the variables

-6m+1/m+5/m+1=0

We multiply all the terms by the denominator


-6m*m+1*m+1+5=0

We add all the numbers together, and all the variables

m-6m*m+6=0

Wy multiply elements

-6m^2+m+6=0

a = -6; b = 1; c = +6;
Δ = b2-4ac
Δ = 12-4·(-6)·6
Δ = 145
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{145}}{2*-6}=\frac{-1-\sqrt{145}}{-12}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{145}}{2*-6}=\frac{-1+\sqrt{145}}{-12}
$