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2/3x-7+5/6x=9
We move all terms to the left:
2/3x-7+5/6x-(9)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: 6x!=0We add all the numbers together, and all the variables
x!=0/6
x!=0
x∈R
2/3x+5/6x-16=0
We calculate fractions
12x/18x^2+15x/18x^2-16=0
We multiply all the terms by the denominator
12x+15x-16*18x^2=0
We add all the numbers together, and all the variables
27x-16*18x^2=0
Wy multiply elements
-288x^2+27x=0
a = -288; b = 27; c = 0;
Δ = b2-4ac
Δ = 272-4·(-288)·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{729}=27$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-27}{2*-288}=\frac{-54}{-576} =3/32 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+27}{2*-288}=\frac{0}{-576} =0 $
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