1/3m-7=-1+3m

Solution for 1/3m-7=-1+3m equation:

1/3m-7=-1+3m

We move all terms to the left:

1/3m-7-(-1+3m)=0


Domain of the equation: 3m!=0

m!=0/3

m!=0

m∈R


We add all the numbers together, and all the variables

1/3m-(3m-1)-7=0

We get rid of parentheses

1/3m-3m+1-7=0

We multiply all the terms by the denominator


-3m*3m+1*3m-7*3m+1=0

Wy multiply elements

-9m^2+3m-21m+1=0

We add all the numbers together, and all the variables

-9m^2-18m+1=0

a = -9; b = -18; c = +1;
Δ = b2-4ac
Δ = -182-4·(-9)·1
Δ = 360
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:

$\sqrt{\Delta}=\sqrt{360}=\sqrt{36*10}=\sqrt{36}*\sqrt{10}=6\sqrt{10}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{10}}{2*-9}=\frac{18-6\sqrt{10}}{-18}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{10}}{2*-9}=\frac{18+6\sqrt{10}}{-18}
$