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5/2x-(1/x)=6
We move all terms to the left:
5/2x-(1/x)-(6)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
5/2x-(+1/x)-6=0
We get rid of parentheses
5/2x-1/x-6=0
We calculate fractions
5x/2x^2+(-2x)/2x^2-6=0
We multiply all the terms by the denominator
5x+(-2x)-6*2x^2=0
Wy multiply elements
-12x^2+5x+(-2x)=0
We get rid of parentheses
-12x^2+5x-2x=0
We add all the numbers together, and all the variables
-12x^2+3x=0
a = -12; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-12)·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$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*-12}=\frac{-6}{-24} =1/4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-12}=\frac{0}{-24} =0 $
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