1/3m-16m=-1

Solution for 1/3m-16m=-1 equation:

1/3m-16m=-1

We move all terms to the left:

1/3m-16m-(-1)=0


Domain of the equation: 3m!=0

m!=0/3

m!=0

m∈R


We add all the numbers together, and all the variables

-16m+1/3m+1=0

We multiply all the terms by the denominator


-16m*3m+1*3m+1=0

Wy multiply elements

-48m^2+3m+1=0

a = -48; b = 3; c = +1;
Δ = b2-4ac
Δ = 32-4·(-48)·1
Δ = 201
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{-(3)-\sqrt{201}}{2*-48}=\frac{-3-\sqrt{201}}{-96}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{201}}{2*-48}=\frac{-3+\sqrt{201}}{-96}
$