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7/8m+5-2/9m=52
We move all terms to the left:
7/8m+5-2/9m-(52)=0
Domain of the equation: 8m!=0
m!=0/8
m!=0
m∈R
Domain of the equation: 9m!=0We add all the numbers together, and all the variables
m!=0/9
m!=0
m∈R
7/8m-2/9m-47=0
We calculate fractions
63m/72m^2+(-16m)/72m^2-47=0
We multiply all the terms by the denominator
63m+(-16m)-47*72m^2=0
Wy multiply elements
-3384m^2+63m+(-16m)=0
We get rid of parentheses
-3384m^2+63m-16m=0
We add all the numbers together, and all the variables
-3384m^2+47m=0
a = -3384; b = 47; c = 0;
Δ = b2-4ac
Δ = 472-4·(-3384)·0
Δ = 2209
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{2209}=47$$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(47)-47}{2*-3384}=\frac{-94}{-6768} =1/72 $$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(47)+47}{2*-3384}=\frac{0}{-6768} =0 $
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