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(8x-3/3x=2)
We move all terms to the left:
(8x-3/3x-(2))=0
Domain of the equation: 3x-2)!=0We get rid of parentheses
x∈R
8x-3/3x-2=0
We multiply all the terms by the denominator
8x*3x-2*3x-3=0
Wy multiply elements
24x^2-6x-3=0
a = 24; b = -6; c = -3;
Δ = b2-4ac
Δ = -62-4·24·(-3)
Δ = 324
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{324}=18$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-18}{2*24}=\frac{-12}{48} =-1/4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+18}{2*24}=\frac{24}{48} =1/2 $
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