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5/2x-9=2+2/3x
We move all terms to the left:
5/2x-9-(2+2/3x)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: 3x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
5/2x-(2/3x+2)-9=0
We get rid of parentheses
5/2x-2/3x-2-9=0
We calculate fractions
15x/6x^2+(-4x)/6x^2-2-9=0
We add all the numbers together, and all the variables
15x/6x^2+(-4x)/6x^2-11=0
We multiply all the terms by the denominator
15x+(-4x)-11*6x^2=0
Wy multiply elements
-66x^2+15x+(-4x)=0
We get rid of parentheses
-66x^2+15x-4x=0
We add all the numbers together, and all the variables
-66x^2+11x=0
a = -66; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-66)·0
Δ = 121
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{121}=11$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-66}=\frac{-22}{-132} =1/6 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-66}=\frac{0}{-132} =0 $
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