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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We calculate fractions


4m/8m^2+6m/8m^2-2-3=0

We add all the numbers together, and all the variables

4m/8m^2+6m/8m^2-5=0

We multiply all the terms by the denominator


4m+6m-5*8m^2=0

We add all the numbers together, and all the variables

10m-5*8m^2=0

Wy multiply elements

-40m^2+10m=0

a = -40; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-40)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*-40}=\frac{-20}{-80}
=1/4
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-40}=\frac{0}{-80}
=0
$