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3x-2/x+1=-12
We move all terms to the left:
3x-2/x+1-(-12)=0
Domain of the equation: x!=0We add all the numbers together, and all the variables
x∈R
3x-2/x+13=0
We multiply all the terms by the denominator
3x*x+13*x-2=0
We add all the numbers together, and all the variables
13x+3x*x-2=0
Wy multiply elements
3x^2+13x-2=0
a = 3; b = 13; c = -2;
Δ = b2-4ac
Δ = 132-4·3·(-2)
Δ = 193
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{-(13)-\sqrt{193}}{2*3}=\frac{-13-\sqrt{193}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{193}}{2*3}=\frac{-13+\sqrt{193}}{6} $
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