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3/x+4=8/3x
We move all terms to the left:
3/x+4-(8/3x)=0
Domain of the equation: x!=0
x∈R
Domain of the equation: 3x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
3/x-(+8/3x)+4=0
We get rid of parentheses
3/x-8/3x+4=0
We calculate fractions
9x/3x^2+(-8x)/3x^2+4=0
We multiply all the terms by the denominator
9x+(-8x)+4*3x^2=0
Wy multiply elements
12x^2+9x+(-8x)=0
We get rid of parentheses
12x^2+9x-8x=0
We add all the numbers together, and all the variables
12x^2+x=0
a = 12; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·12·0
Δ = 1
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{1}=1$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*12}=\frac{-2}{24} =-1/12 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*12}=\frac{0}{24} =0 $
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