3/m=9/2m+4

Solution for 3/m=9/2m+4 equation:

3/m=9/2m+4

We move all terms to the left:

3/m-(9/2m+4)=0


Domain of the equation: m!=0

m∈R



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

m∈R


We get rid of parentheses

3/m-9/2m-4=0

We calculate fractions


6m/2m^2+(-9m)/2m^2-4=0

We multiply all the terms by the denominator


6m+(-9m)-4*2m^2=0

Wy multiply elements

-8m^2+6m+(-9m)=0

We get rid of parentheses

-8m^2+6m-9m=0

We add all the numbers together, and all the variables

-8m^2-3m=0

a = -8; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·(-8)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*-8}=\frac{0}{-16}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*-8}=\frac{6}{-16}
=-3/8
$