16/6m+8/3m-4/6m-4/3m=1

Solution for 16/6m+8/3m-4/6m-4/3m=1 equation:

16/6m+8/3m-4/6m-4/3m=1

We move all terms to the left:

16/6m+8/3m-4/6m-4/3m-(1)=0


Domain of the equation: 6m!=0

m!=0/6

m!=0

m∈R



Domain of the equation: 3m!=0

m!=0/3

m!=0

m∈R


We calculate fractions


(-12m+16)/18m^2+(-24m+8)/18m^2-1=0

We multiply all the terms by the denominator


(-12m+16)+(-24m+8)-1*18m^2=0

Wy multiply elements

-18m^2+(-12m+16)+(-24m+8)=0

We get rid of parentheses

-18m^2-12m-24m+16+8=0

We add all the numbers together, and all the variables

-18m^2-36m+24=0

a = -18; b = -36; c = +24;
Δ = b2-4ac
Δ = -362-4·(-18)·24
Δ = 3024
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:

$\sqrt{\Delta}=\sqrt{3024}=\sqrt{144*21}=\sqrt{144}*\sqrt{21}=12\sqrt{21}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-12\sqrt{21}}{2*-18}=\frac{36-12\sqrt{21}}{-36}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+12\sqrt{21}}{2*-18}=\frac{36+12\sqrt{21}}{-36}
$