4/x-5=6/2x+1

Solution for 4/x-5=6/2x+1 equation:

4/x-5=6/2x+1

We move all terms to the left:

4/x-5-(6/2x+1)=0


Domain of the equation: x!=0

x∈R



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

x∈R


We get rid of parentheses

4/x-6/2x-1-5=0

We calculate fractions


8x/2x^2+(-6x)/2x^2-1-5=0

We add all the numbers together, and all the variables

8x/2x^2+(-6x)/2x^2-6=0

We multiply all the terms by the denominator


8x+(-6x)-6*2x^2=0

Wy multiply elements

-12x^2+8x+(-6x)=0

We get rid of parentheses

-12x^2+8x-6x=0

We add all the numbers together, and all the variables

-12x^2+2x=0

a = -12; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-12)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-12}=\frac{-4}{-24}
=1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-12}=\frac{0}{-24}
=0
$