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5/6e-2/3e=-24
We move all terms to the left:
5/6e-2/3e-(-24)=0
Domain of the equation: 6e!=0
e!=0/6
e!=0
e∈R
Domain of the equation: 3e!=0We add all the numbers together, and all the variables
e!=0/3
e!=0
e∈R
5/6e-2/3e+24=0
We calculate fractions
15e/18e^2+(-12e)/18e^2+24=0
We multiply all the terms by the denominator
15e+(-12e)+24*18e^2=0
Wy multiply elements
432e^2+15e+(-12e)=0
We get rid of parentheses
432e^2+15e-12e=0
We add all the numbers together, and all the variables
432e^2+3e=0
a = 432; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·432·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{9}=3$$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*432}=\frac{-6}{864} =-1/144 $$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*432}=\frac{0}{864} =0 $
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