1/6m-21=-1/2m+5

Solution for 1/6m-21=-1/2m+5 equation:

1/6m-21=-1/2m+5

We move all terms to the left:

1/6m-21-(-1/2m+5)=0


Domain of the equation: 6m!=0

m!=0/6

m!=0

m∈R



Domain of the equation: 2m+5)!=0

m∈R


We get rid of parentheses

1/6m+1/2m-5-21=0

We calculate fractions


2m/12m^2+6m/12m^2-5-21=0

We add all the numbers together, and all the variables

2m/12m^2+6m/12m^2-26=0

We multiply all the terms by the denominator


2m+6m-26*12m^2=0

We add all the numbers together, and all the variables

8m-26*12m^2=0

Wy multiply elements

-312m^2+8m=0

a = -312; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·(-312)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*-312}=\frac{-16}{-624}
=1/39
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*-312}=\frac{0}{-624}
=0
$