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12.6/x+1=x
We move all terms to the left:
12.6/x+1-(x)=0
Domain of the equation: x!=0We add all the numbers together, and all the variables
x∈R
-1x+12.6/x+1=0
We multiply all the terms by the denominator
-1x*x+1*x+12.6=0
We add all the numbers together, and all the variables
x-1x*x+12.6=0
Wy multiply elements
-1x^2+x+12.6=0
a = -1; b = 1; c = +12.6;
Δ = b2-4ac
Δ = 12-4·(-1)·12.6
Δ = 51.4
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{-(1)-\sqrt{51.4}}{2*-1}=\frac{-1-\sqrt{51.4}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{51.4}}{2*-1}=\frac{-1+\sqrt{51.4}}{-2} $
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