2/3m-9=1/2m+21

Solution for 2/3m-9=1/2m+21 equation:

2/3m-9=1/2m+21

We move all terms to the left:

2/3m-9-(1/2m+21)=0


Domain of the equation: 3m!=0

m!=0/3

m!=0

m∈R



Domain of the equation: 2m+21)!=0

m∈R


We get rid of parentheses

2/3m-1/2m-21-9=0

We calculate fractions


4m/6m^2+(-3m)/6m^2-21-9=0

We add all the numbers together, and all the variables

4m/6m^2+(-3m)/6m^2-30=0

We multiply all the terms by the denominator


4m+(-3m)-30*6m^2=0

Wy multiply elements

-180m^2+4m+(-3m)=0

We get rid of parentheses

-180m^2+4m-3m=0

We add all the numbers together, and all the variables

-180m^2+m=0

a = -180; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-180)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-180}=\frac{-2}{-360}
=1/180
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-180}=\frac{0}{-360}
=0
$