5-2x=1/x-4

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

5-2x=1/x-4

We move all terms to the left:

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


Domain of the equation: x-4)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


-2x*x+4*x+5*x-1=0

We add all the numbers together, and all the variables

9x-2x*x-1=0

Wy multiply elements

-2x^2+9x-1=0

a = -2; b = 9; c = -1;
Δ = b2-4ac
Δ = 92-4·(-2)·(-1)
Δ = 73
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{-(9)-\sqrt{73}}{2*-2}=\frac{-9-\sqrt{73}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{73}}{2*-2}=\frac{-9+\sqrt{73}}{-4}
$