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8x-2/3x=3
We move all terms to the left:
8x-2/3x-(3)=0
Domain of the equation: 3x!=0We multiply all the terms by the denominator
x!=0/3
x!=0
x∈R
8x*3x-3*3x-2=0
Wy multiply elements
24x^2-9x-2=0
a = 24; b = -9; c = -2;
Δ = b2-4ac
Δ = -92-4·24·(-2)
Δ = 273
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{273}}{2*24}=\frac{9-\sqrt{273}}{48} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{273}}{2*24}=\frac{9+\sqrt{273}}{48} $
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