1/3m-2=3m-18

Solution for 1/3m-2=3m-18 equation:

1/3m-2=3m-18

We move all terms to the left:

1/3m-2-(3m-18)=0


Domain of the equation: 3m!=0

m!=0/3

m!=0

m∈R


We get rid of parentheses

1/3m-3m+18-2=0

We multiply all the terms by the denominator


-3m*3m+18*3m-2*3m+1=0

Wy multiply elements

-9m^2+54m-6m+1=0

We add all the numbers together, and all the variables

-9m^2+48m+1=0

a = -9; b = 48; c = +1;
Δ = b2-4ac
Δ = 482-4·(-9)·1
Δ = 2340
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:

$\sqrt{\Delta}=\sqrt{2340}=\sqrt{36*65}=\sqrt{36}*\sqrt{65}=6\sqrt{65}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-6\sqrt{65}}{2*-9}=\frac{-48-6\sqrt{65}}{-18}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+6\sqrt{65}}{2*-9}=\frac{-48+6\sqrt{65}}{-18}
$