1/x-2=4-x

Solution for 1/x-2=4-x equation:

1/x-2=4-x

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

1/x-(-1x+4)-2=0

We get rid of parentheses

1/x+1x-4-2=0

We multiply all the terms by the denominator


1x*x-4*x-2*x+1=0

We add all the numbers together, and all the variables

-6x+1x*x+1=0

Wy multiply elements

x^2-6x+1=0

a = 1; b = -6; c = +1;
Δ = b2-4ac
Δ = -62-4·1·1
Δ = 32
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:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-4\sqrt{2}}{2*1}=\frac{6-4\sqrt{2}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+4\sqrt{2}}{2*1}=\frac{6+4\sqrt{2}}{2}
$