1/2m-3=3-1/4m

Solution for 1/2m-3=3-1/4m equation:

1/2m-3=3-1/4m

We move all terms to the left:

1/2m-3-(3-1/4m)=0


Domain of the equation: 2m!=0

m!=0/2

m!=0

m∈R



Domain of the equation: 4m)!=0

m!=0/1

m!=0

m∈R


We add all the numbers together, and all the variables

1/2m-(-1/4m+3)-3=0

We get rid of parentheses

1/2m+1/4m-3-3=0

We calculate fractions


4m/8m^2+2m/8m^2-3-3=0

We add all the numbers together, and all the variables

4m/8m^2+2m/8m^2-6=0

We multiply all the terms by the denominator


4m+2m-6*8m^2=0

We add all the numbers together, and all the variables

6m-6*8m^2=0

Wy multiply elements

-48m^2+6m=0

a = -48; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-48)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*-48}=\frac{-12}{-96}
=1/8
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-48}=\frac{0}{-96}
=0
$