4/x-10=x

Solution for 4/x-10=x equation:

4/x-10=x

We move all terms to the left:

4/x-10-(x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-1x+4/x-10=0

We multiply all the terms by the denominator


-1x*x-10*x+4=0

We add all the numbers together, and all the variables

-10x-1x*x+4=0

Wy multiply elements

-1x^2-10x+4=0

a = -1; b = -10; c = +4;
Δ = b2-4ac
Δ = -102-4·(-1)·4
Δ = 116
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:

$\sqrt{\Delta}=\sqrt{116}=\sqrt{4*29}=\sqrt{4}*\sqrt{29}=2\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{29}}{2*-1}=\frac{10-2\sqrt{29}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{29}}{2*-1}=\frac{10+2\sqrt{29}}{-2}
$