5+2x=1/2x-1

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

5+2x=1/2x-1

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

4x^2+2x+10x-1=0

We add all the numbers together, and all the variables

4x^2+12x-1=0

a = 4; b = 12; c = -1;
Δ = b2-4ac
Δ = 122-4·4·(-1)
Δ = 160
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:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{10}}{2*4}=\frac{-12-4\sqrt{10}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{10}}{2*4}=\frac{-12+4\sqrt{10}}{8}
$