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8m-3/3m=2
We move all terms to the left:
8m-3/3m-(2)=0
Domain of the equation: 3m!=0We multiply all the terms by the denominator
m!=0/3
m!=0
m∈R
8m*3m-2*3m-3=0
Wy multiply elements
24m^2-6m-3=0
a = 24; b = -6; c = -3;
Δ = b2-4ac
Δ = -62-4·24·(-3)
Δ = 324
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{324}=18$$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-18}{2*24}=\frac{-12}{48} =-1/4 $$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+18}{2*24}=\frac{24}{48} =1/2 $
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