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X-2/X-6=-1
We move all terms to the left:
X-2/X-6-(-1)=0
Domain of the equation: X!=0We add all the numbers together, and all the variables
X∈R
X-2/X-5=0
We multiply all the terms by the denominator
X*X-5*X-2=0
We add all the numbers together, and all the variables
-5X+X*X-2=0
Wy multiply elements
X^2-5X-2=0
a = 1; b = -5; c = -2;
Δ = b2-4ac
Δ = -52-4·1·(-2)
Δ = 33
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{-(-5)-\sqrt{33}}{2*1}=\frac{5-\sqrt{33}}{2} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{33}}{2*1}=\frac{5+\sqrt{33}}{2} $
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