2/x-30=x

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Solution for 2/x-30=x equation:



2/x-30=x
We move all terms to the left:
2/x-30-(x)=0
Domain of the equation: x!=0
x∈R
We add all the numbers together, and all the variables
-1x+2/x-30=0
We multiply all the terms by the denominator
-1x*x-30*x+2=0
We add all the numbers together, and all the variables
-30x-1x*x+2=0
Wy multiply elements
-1x^2-30x+2=0
a = -1; b = -30; c = +2;
Δ = b2-4ac
Δ = -302-4·(-1)·2
Δ = 908
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:
$\sqrt{\Delta}=\sqrt{908}=\sqrt{4*227}=\sqrt{4}*\sqrt{227}=2\sqrt{227}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{227}}{2*-1}=\frac{30-2\sqrt{227}}{-2} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{227}}{2*-1}=\frac{30+2\sqrt{227}}{-2} $

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