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2x+3/2-3x/x-3=x
We move all terms to the left:
2x+3/2-3x/x-3-(x)=0
Domain of the equation: x!=0We add all the numbers together, and all the variables
x∈R
x-3x/x-3+3/2=0
We calculate fractions
x+(-6x)/2x+3x/2x-3=0
We multiply all the terms by the denominator
x*2x+(-6x)+3x-3*2x=0
We add all the numbers together, and all the variables
3x+x*2x+(-6x)-3*2x=0
Wy multiply elements
2x^2+3x+(-6x)-6x=0
We get rid of parentheses
2x^2+3x-6x-6x=0
We add all the numbers together, and all the variables
2x^2-9x=0
a = 2; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·2·0
Δ = 81
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{81}=9$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*2}=\frac{0}{4} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*2}=\frac{18}{4} =4+1/2 $
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