6-1/6m-8=0m

Solution for 6-1/6m-8=0m equation:

6-1/6m-8=0m

We move all terms to the left:

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


Domain of the equation: 6m!=0

m!=0/6

m!=0

m∈R


We add all the numbers together, and all the variables

-1m-1/6m-2=0

We multiply all the terms by the denominator


-1m*6m-2*6m-1=0

Wy multiply elements

-6m^2-12m-1=0

a = -6; b = -12; c = -1;
Δ = b2-4ac
Δ = -122-4·(-6)·(-1)
Δ = 120
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:

$\sqrt{\Delta}=\sqrt{120}=\sqrt{4*30}=\sqrt{4}*\sqrt{30}=2\sqrt{30}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{30}}{2*-6}=\frac{12-2\sqrt{30}}{-12}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{30}}{2*-6}=\frac{12+2\sqrt{30}}{-12}
$