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

Solution for 5/x-4-2/1-x=0 equation:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-1x+5/x-6=0

We multiply all the terms by the denominator


-1x*x-6*x+5=0

We add all the numbers together, and all the variables

-6x-1x*x+5=0

Wy multiply elements

-1x^2-6x+5=0

a = -1; b = -6; c = +5;
Δ = b2-4ac
Δ = -62-4·(-1)·5
Δ = 56
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:

$\sqrt{\Delta}=\sqrt{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{14}}{2*-1}=\frac{6-2\sqrt{14}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{14}}{2*-1}=\frac{6+2\sqrt{14}}{-2}
$