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1/9x+1/2x+1/9=19/6
We move all terms to the left:
1/9x+1/2x+1/9-(19/6)=0
Domain of the equation: 9x!=0
x!=0/9
x!=0
x∈R
Domain of the equation: 2x!=0We add all the numbers together, and all the variables
x!=0/2
x!=0
x∈R
1/9x+1/2x+1/9-(+19/6)=0
We get rid of parentheses
1/9x+1/2x+1/9-19/6=0
We calculate fractions
(-6156x^2)/8748x^2+72x/8748x^2+4374x/8748x^2+72x/8748x^2=0
We multiply all the terms by the denominator
(-6156x^2)+72x+4374x+72x=0
We add all the numbers together, and all the variables
(-6156x^2)+4518x=0
We get rid of parentheses
-6156x^2+4518x=0
a = -6156; b = 4518; c = 0;
Δ = b2-4ac
Δ = 45182-4·(-6156)·0
Δ = 20412324
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{20412324}=4518$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4518)-4518}{2*-6156}=\frac{-9036}{-12312} =251/342 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4518)+4518}{2*-6156}=\frac{0}{-12312} =0 $
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