4/9m-1/3m+1/2=5/18

Solution for 4/9m-1/3m+1/2=5/18 equation:

4/9m-1/3m+1/2=5/18

We move all terms to the left:

4/9m-1/3m+1/2-(5/18)=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

4/9m-1/3m+1/2-(+5/18)=0

We get rid of parentheses

4/9m-1/3m+1/2-5/18=0

We calculate fractions


(-810m^2)/1944m^2+1458m^2/1944m^2+864m/1944m^2+(-648m)/1944m^2=0

We multiply all the terms by the denominator


(-810m^2)+1458m^2+864m+(-648m)=0

We add all the numbers together, and all the variables

1458m^2+(-810m^2)+864m+(-648m)=0

We get rid of parentheses

1458m^2-810m^2+864m-648m=0

We add all the numbers together, and all the variables

648m^2+216m=0

a = 648; b = 216; c = 0;
Δ = b2-4ac
Δ = 2162-4·648·0
Δ = 46656
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{46656}=216$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(216)-216}{2*648}=\frac{-432}{1296}
=-1/3
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(216)+216}{2*648}=\frac{0}{1296}
=0
$