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6/2x+5=4/x-9

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Solution for 6/2x+5=4/x-9 equation:



6/2x+5=4/x-9
We move all terms to the left:
6/2x+5-(4/x-9)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: x-9)!=0
x∈R
We get rid of parentheses
6/2x-4/x+9+5=0
We calculate fractions
6x/2x^2+(-8x)/2x^2+9+5=0
We add all the numbers together, and all the variables
6x/2x^2+(-8x)/2x^2+14=0
We multiply all the terms by the denominator
6x+(-8x)+14*2x^2=0
Wy multiply elements
28x^2+6x+(-8x)=0
We get rid of parentheses
28x^2+6x-8x=0
We add all the numbers together, and all the variables
28x^2-2x=0
a = 28; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·28·0
Δ = 4
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{4}=2
x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2}{2*28}=\frac{0}{56} =0
x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*28}=\frac{4}{56} =1/14

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