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x+2/x=18
We move all terms to the left:
x+2/x-(18)=0
Domain of the equation: x!=0We multiply all the terms by the denominator
x∈R
x*x-18*x+2=0
We add all the numbers together, and all the variables
-18x+x*x+2=0
Wy multiply elements
x^2-18x+2=0
a = 1; b = -18; c = +2;
Δ = b2-4ac
Δ = -182-4·1·2
Δ = 316
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{316}=\sqrt{4*79}=\sqrt{4}*\sqrt{79}=2\sqrt{79}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{79}}{2*1}=\frac{18-2\sqrt{79}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{79}}{2*1}=\frac{18+2\sqrt{79}}{2} $
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