0.5/x-2=x-4

Solution for 0.5/x-2=x-4 equation:

0.5/x-2=x-4

We move all terms to the left:

0.5/x-2-(x-4)=0


Domain of the equation: x!=0

x∈R


We get rid of parentheses

0.5/x-x+4-2=0

We multiply all the terms by the denominator


-x*x+4*x-2*x+0.5=0

We add all the numbers together, and all the variables

2x-x*x+0.5=0

Wy multiply elements

-1x^2+2x+0.5=0

a = -1; b = 2; c = +0.5;
Δ = b2-4ac
Δ = 22-4·(-1)·0.5
Δ = 6
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-\sqrt{6}}{2*-1}=\frac{-2-\sqrt{6}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+\sqrt{6}}{2*-1}=\frac{-2+\sqrt{6}}{-2}
$