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1/3x-8/x=11
We move all terms to the left:
1/3x-8/x-(11)=0
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
Domain of the equation: x!=0We calculate fractions
x∈R
x/3x^2+(-24x)/3x^2-11=0
We multiply all the terms by the denominator
x+(-24x)-11*3x^2=0
Wy multiply elements
-33x^2+x+(-24x)=0
We get rid of parentheses
-33x^2+x-24x=0
We add all the numbers together, and all the variables
-33x^2-23x=0
a = -33; b = -23; c = 0;
Δ = b2-4ac
Δ = -232-4·(-33)·0
Δ = 529
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{529}=23$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-23}{2*-33}=\frac{0}{-66} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+23}{2*-33}=\frac{46}{-66} =-23/33 $
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