2/2x+1=3/x+6

Solution for 2/2x+1=3/x+6 equation:

2/2x+1=3/x+6

We move all terms to the left:

2/2x+1-(3/x+6)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: x+6)!=0

x∈R


We get rid of parentheses

2/2x-3/x-6+1=0

We calculate fractions


2x/2x^2+(-6x)/2x^2-6+1=0

We add all the numbers together, and all the variables

2x/2x^2+(-6x)/2x^2-5=0

We multiply all the terms by the denominator


2x+(-6x)-5*2x^2=0

Wy multiply elements

-10x^2+2x+(-6x)=0

We get rid of parentheses

-10x^2+2x-6x=0

We add all the numbers together, and all the variables

-10x^2-4x=0

a = -10; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-10)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*-10}=\frac{0}{-20}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-10}=\frac{8}{-20}
=-2/5
$