-1/3m-7=m

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

-1/3m-7=m

We move all terms to the left:

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


Domain of the equation: 3m!=0

m!=0/3

m!=0

m∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

a = -3; b = -21; c = -1;
Δ = b2-4ac
Δ = -212-4·(-3)·(-1)
Δ = 429
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-\sqrt{429}}{2*-3}=\frac{21-\sqrt{429}}{-6}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+\sqrt{429}}{2*-3}=\frac{21+\sqrt{429}}{-6}
$