4/x-6=4/2x+3

Solution for 4/x-6=4/2x+3 equation:

4/x-6=4/2x+3

We move all terms to the left:

4/x-6-(4/2x+3)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x+3)!=0

x∈R


We get rid of parentheses

4/x-4/2x-3-6=0

We calculate fractions


8x/2x^2+(-4x)/2x^2-3-6=0

We add all the numbers together, and all the variables

8x/2x^2+(-4x)/2x^2-9=0

We multiply all the terms by the denominator


8x+(-4x)-9*2x^2=0

Wy multiply elements

-18x^2+8x+(-4x)=0

We get rid of parentheses

-18x^2+8x-4x=0

We add all the numbers together, and all the variables

-18x^2+4x=0

a = -18; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·(-18)·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*-18}=\frac{-8}{-36}
=2/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*-18}=\frac{0}{-36}
=0
$