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2x+2/x=10
We move all terms to the left:
2x+2/x-(10)=0
Domain of the equation: x!=0We multiply all the terms by the denominator
x∈R
2x*x-10*x+2=0
We add all the numbers together, and all the variables
-10x+2x*x+2=0
Wy multiply elements
2x^2-10x+2=0
a = 2; b = -10; c = +2;
Δ = b2-4ac
Δ = -102-4·2·2
Δ = 84
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{21}}{2*2}=\frac{10-2\sqrt{21}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{21}}{2*2}=\frac{10+2\sqrt{21}}{4} $
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