m-9/4+3=m/3m=

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

m-9/4+3=m/3m=

We move all terms to the left:

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


Domain of the equation: 3m)!=0

m!=0/1

m!=0

m∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


m+(-4m)/12m+(-27m)/12m+3=0

We multiply all the terms by the denominator


m*12m+(-4m)+(-27m)+3*12m=0

Wy multiply elements

12m^2+(-4m)+(-27m)+36m=0

We get rid of parentheses

12m^2-4m-27m+36m=0

We add all the numbers together, and all the variables

12m^2+5m=0

a = 12; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·12·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*12}=\frac{-10}{24}
=-5/12
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*12}=\frac{0}{24}
=0
$