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2/3m+1/4m=25
We move all terms to the left:
2/3m+1/4m-(25)=0
Domain of the equation: 3m!=0
m!=0/3
m!=0
m∈R
Domain of the equation: 4m!=0We calculate fractions
m!=0/4
m!=0
m∈R
8m/12m^2+3m/12m^2-25=0
We multiply all the terms by the denominator
8m+3m-25*12m^2=0
We add all the numbers together, and all the variables
11m-25*12m^2=0
Wy multiply elements
-300m^2+11m=0
a = -300; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-300)·0
Δ = 121
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{121}=11$$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-300}=\frac{-22}{-600} =11/300 $$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-300}=\frac{0}{-600} =0 $
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