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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x-4+1)!=0

We move all terms containing x to the left, all other terms to the right

2x+1)!=4

x∈R


We add all the numbers together, and all the variables

-5/x-(-1/2x-3)-2=0

We get rid of parentheses

-5/x+1/2x+3-2=0

We calculate fractions


(-10x)/2x^2+x/2x^2+3-2=0

We add all the numbers together, and all the variables

(-10x)/2x^2+x/2x^2+1=0

We multiply all the terms by the denominator


(-10x)+x+1*2x^2=0

We add all the numbers together, and all the variables

x+(-10x)+1*2x^2=0

Wy multiply elements

2x^2+x+(-10x)=0

We get rid of parentheses

2x^2+x-10x=0

We add all the numbers together, and all the variables

2x^2-9x=0

a = 2; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·2·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*2}=\frac{0}{4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*2}=\frac{18}{4}
=4+1/2
$