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

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

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

4/x-2/2x-9=0

We calculate fractions


8x/2x^2+(-2x)/2x^2-9=0

We multiply all the terms by the denominator


8x+(-2x)-9*2x^2=0

Wy multiply elements

-18x^2+8x+(-2x)=0

We get rid of parentheses

-18x^2+8x-2x=0

We add all the numbers together, and all the variables

-18x^2+6x=0

a = -18; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-18)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*-18}=\frac{-12}{-36}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-18}=\frac{0}{-36}
=0
$