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-3/8m+1-3/18m=5
We move all terms to the left:
-3/8m+1-3/18m-(5)=0
Domain of the equation: 8m!=0
m!=0/8
m!=0
m∈R
Domain of the equation: 18m!=0We add all the numbers together, and all the variables
m!=0/18
m!=0
m∈R
-3/8m-3/18m-4=0
We calculate fractions
(-54m)/144m^2+(-24m)/144m^2-4=0
We multiply all the terms by the denominator
(-54m)+(-24m)-4*144m^2=0
Wy multiply elements
-576m^2+(-54m)+(-24m)=0
We get rid of parentheses
-576m^2-54m-24m=0
We add all the numbers together, and all the variables
-576m^2-78m=0
a = -576; b = -78; c = 0;
Δ = b2-4ac
Δ = -782-4·(-576)·0
Δ = 6084
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{6084}=78$$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-78)-78}{2*-576}=\frac{0}{-1152} =0 $$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-78)+78}{2*-576}=\frac{156}{-1152} =-13/96 $
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