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5x-2/2x+1=5x-12/6x-1
We move all terms to the left:
5x-2/2x+1-(5x-12/6x-1)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: 6x-1)!=0We get rid of parentheses
x∈R
5x-2/2x-5x+12/6x+1+1=0
We calculate fractions
5x-5x+(-12x)/12x^2+24x/12x^2+1+1=0
We add all the numbers together, and all the variables
(-12x)/12x^2+24x/12x^2+2=0
We multiply all the terms by the denominator
(-12x)+24x+2*12x^2=0
We add all the numbers together, and all the variables
24x+(-12x)+2*12x^2=0
Wy multiply elements
24x^2+24x+(-12x)=0
We get rid of parentheses
24x^2+24x-12x=0
We add all the numbers together, and all the variables
24x^2+12x=0
a = 24; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·24·0
Δ = 144
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{144}=12$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12}{2*24}=\frac{-24}{48} =-1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*24}=\frac{0}{48} =0 $
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