2/x-30=x

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}
$