5/2m-1/4=8/3m

Solution for 5/2m-1/4=8/3m equation:

5/2m-1/4=8/3m

We move all terms to the left:

5/2m-1/4-(8/3m)=0


Domain of the equation: 2m!=0

m!=0/2

m!=0

m∈R



Domain of the equation: 3m)!=0

m!=0/1

m!=0

m∈R


We add all the numbers together, and all the variables

5/2m-(+8/3m)-1/4=0

We get rid of parentheses

5/2m-8/3m-1/4=0

We calculate fractions


(-18m^2)/96m^2+240m/96m^2+(-256m)/96m^2=0

We multiply all the terms by the denominator


(-18m^2)+240m+(-256m)=0

We get rid of parentheses

-18m^2+240m-256m=0

We add all the numbers together, and all the variables

-18m^2-16m=0

a = -18; b = -16; c = 0;
Δ = b2-4ac
Δ = -162-4·(-18)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-16}{2*-18}=\frac{0}{-36}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16}{2*-18}=\frac{32}{-36}
=-8/9
$