(5)/(9)m-1-(1)/(3)m=3

Solution for (5)/(9)m-1-(1)/(3)m=3 equation:

(5)/(9)m-1-(1)/(3)m=3

We move all terms to the left:

(5)/(9)m-1-(1)/(3)m-(3)=0


Domain of the equation: 9m!=0

m!=0/9

m!=0

m∈R



Domain of the equation: 3m!=0

m!=0/3

m!=0

m∈R


We add all the numbers together, and all the variables

5/9m-1/3m-4=0

We calculate fractions


15m/27m^2+(-9m)/27m^2-4=0

We multiply all the terms by the denominator


15m+(-9m)-4*27m^2=0

Wy multiply elements

-108m^2+15m+(-9m)=0

We get rid of parentheses

-108m^2+15m-9m=0

We add all the numbers together, and all the variables

-108m^2+6m=0

a = -108; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-108)·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*-108}=\frac{-12}{-216}
=1/18
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-108}=\frac{0}{-216}
=0
$