x+2=10/x

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Solution for x+2=10/x equation:



x+2=10/x
We move all terms to the left:
x+2-(10/x)=0
Domain of the equation: x)!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
x-(+10/x)+2=0
We get rid of parentheses
x-10/x+2=0
We multiply all the terms by the denominator
x*x+2*x-10=0
We add all the numbers together, and all the variables
2x+x*x-10=0
Wy multiply elements
x^2+2x-10=0
a = 1; b = 2; c = -10;
Δ = b2-4ac
Δ = 22-4·1·(-10)
Δ = 44
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:
$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{11}}{2*1}=\frac{-2-2\sqrt{11}}{2} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{11}}{2*1}=\frac{-2+2\sqrt{11}}{2} $

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