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x-6/x+2=3
We move all terms to the left:
x-6/x+2-(3)=0
Domain of the equation: x!=0We add all the numbers together, and all the variables
x∈R
x-6/x-1=0
We multiply all the terms by the denominator
x*x-1*x-6=0
We add all the numbers together, and all the variables
-1x+x*x-6=0
Wy multiply elements
x^2-1x-6=0
a = 1; b = -1; c = -6;
Δ = b2-4ac
Δ = -12-4·1·(-6)
Δ = 25
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{25}=5$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-5}{2*1}=\frac{-4}{2} =-2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+5}{2*1}=\frac{6}{2} =3 $
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