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4/x-3+3/2x-6=11
We move all terms to the left:
4/x-3+3/2x-6-(11)=0
Domain of the equation: 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
4/x+3/2x-20=0
We calculate fractions
8x/2x^2+3x/2x^2-20=0
We multiply all the terms by the denominator
8x+3x-20*2x^2=0
We add all the numbers together, and all the variables
11x-20*2x^2=0
Wy multiply elements
-40x^2+11x=0
a = -40; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-40)·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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-40}=\frac{-22}{-80} =11/40 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-40}=\frac{0}{-80} =0 $
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