33/6m-3/2m-6=6

Solution for 33/6m-3/2m-6=6 equation:

33/6m-3/2m-6=6

We move all terms to the left:

33/6m-3/2m-6-(6)=0


Domain of the equation: 6m!=0

m!=0/6

m!=0

m∈R



Domain of the equation: 2m!=0

m!=0/2

m!=0

m∈R


We add all the numbers together, and all the variables

33/6m-3/2m-12=0

We calculate fractions


66m/12m^2+(-18m)/12m^2-12=0

We multiply all the terms by the denominator


66m+(-18m)-12*12m^2=0

Wy multiply elements

-144m^2+66m+(-18m)=0

We get rid of parentheses

-144m^2+66m-18m=0

We add all the numbers together, and all the variables

-144m^2+48m=0

a = -144; b = 48; c = 0;
Δ = b2-4ac
Δ = 482-4·(-144)·0
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-48}{2*-144}=\frac{-96}{-288}
=1/3
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+48}{2*-144}=\frac{0}{-288}
=0
$