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2/3m+2=-3+3/2m
We move all terms to the left:
2/3m+2-(-3+3/2m)=0
Domain of the equation: 3m!=0
m!=0/3
m!=0
m∈R
Domain of the equation: 2m)!=0We add all the numbers together, and all the variables
m!=0/1
m!=0
m∈R
2/3m-(3/2m-3)+2=0
We get rid of parentheses
2/3m-3/2m+3+2=0
We calculate fractions
4m/6m^2+(-9m)/6m^2+3+2=0
We add all the numbers together, and all the variables
4m/6m^2+(-9m)/6m^2+5=0
We multiply all the terms by the denominator
4m+(-9m)+5*6m^2=0
Wy multiply elements
30m^2+4m+(-9m)=0
We get rid of parentheses
30m^2+4m-9m=0
We add all the numbers together, and all the variables
30m^2-5m=0
a = 30; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·30·0
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$$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*30}=\frac{0}{60} =0 $$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*30}=\frac{10}{60} =1/6 $
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