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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



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

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

2x/2x^2+5x/2x^2+4=0

We multiply all the terms by the denominator


2x+5x+4*2x^2=0

We add all the numbers together, and all the variables

7x+4*2x^2=0

Wy multiply elements

8x^2+7x=0

a = 8; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·8·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*8}=\frac{-14}{16}
=-7/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*8}=\frac{0}{16}
=0
$