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12x-4/x=3
We move all terms to the left:
12x-4/x-(3)=0
Domain of the equation: x!=0We multiply all the terms by the denominator
x∈R
12x*x-3*x-4=0
We add all the numbers together, and all the variables
-3x+12x*x-4=0
Wy multiply elements
12x^2-3x-4=0
a = 12; b = -3; c = -4;
Δ = b2-4ac
Δ = -32-4·12·(-4)
Δ = 201
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{-(-3)-\sqrt{201}}{2*12}=\frac{3-\sqrt{201}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{201}}{2*12}=\frac{3+\sqrt{201}}{24} $
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