3-2/9m=1/3m-7

Solution for 3-2/9m=1/3m-7 equation:

3-2/9m=1/3m-7

We move all terms to the left:

3-2/9m-(1/3m-7)=0


Domain of the equation: 9m!=0

m!=0/9

m!=0

m∈R



Domain of the equation: 3m-7)!=0

m∈R


We get rid of parentheses

-2/9m-1/3m+7+3=0

We calculate fractions


(-6m)/27m^2+(-9m)/27m^2+7+3=0

We add all the numbers together, and all the variables

(-6m)/27m^2+(-9m)/27m^2+10=0

We multiply all the terms by the denominator


(-6m)+(-9m)+10*27m^2=0

Wy multiply elements

270m^2+(-6m)+(-9m)=0

We get rid of parentheses

270m^2-6m-9m=0

We add all the numbers together, and all the variables

270m^2-15m=0

a = 270; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·270·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-15}{2*270}=\frac{0}{540}
=0
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*270}=\frac{30}{540}
=1/18
$