1/2m=5/4m+2

Solution for 1/2m=5/4m+2 equation:

1/2m=5/4m+2

We move all terms to the left:

1/2m-(5/4m+2)=0


Domain of the equation: 2m!=0

m!=0/2

m!=0

m∈R



Domain of the equation: 4m+2)!=0

m∈R


We get rid of parentheses

1/2m-5/4m-2=0

We calculate fractions


4m/8m^2+(-10m)/8m^2-2=0

We multiply all the terms by the denominator


4m+(-10m)-2*8m^2=0

Wy multiply elements

-16m^2+4m+(-10m)=0

We get rid of parentheses

-16m^2+4m-10m=0

We add all the numbers together, and all the variables

-16m^2-6m=0

a = -16; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·(-16)·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*-16}=\frac{0}{-32}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*-16}=\frac{12}{-32}
=-3/8
$