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5/x-2=13/2x-13
We move all terms to the left:
5/x-2-(13/2x-13)=0
Domain of the equation: x!=0
x∈R
Domain of the equation: 2x-13)!=0We get rid of parentheses
x∈R
5/x-13/2x+13-2=0
We calculate fractions
10x/2x^2+(-13x)/2x^2+13-2=0
We add all the numbers together, and all the variables
10x/2x^2+(-13x)/2x^2+11=0
We multiply all the terms by the denominator
10x+(-13x)+11*2x^2=0
Wy multiply elements
22x^2+10x+(-13x)=0
We get rid of parentheses
22x^2+10x-13x=0
We add all the numbers together, and all the variables
22x^2-3x=0
a = 22; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·22·0
Δ = 9
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{9}=3$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3}{2*22}=\frac{0}{44} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*22}=\frac{6}{44} =3/22 $
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