2/2x-4-3/x-9=1

Solution for 2/2x-4-3/x-9=1 equation:

2/2x-4-3/x-9=1

We move all terms to the left:

2/2x-4-3/x-9-(1)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

2/2x-3/x-14=0

We calculate fractions


2x/2x^2+(-6x)/2x^2-14=0

We multiply all the terms by the denominator


2x+(-6x)-14*2x^2=0

Wy multiply elements

-28x^2+2x+(-6x)=0

We get rid of parentheses

-28x^2+2x-6x=0

We add all the numbers together, and all the variables

-28x^2-4x=0

a = -28; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-28)·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*-28}=\frac{0}{-56}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-28}=\frac{8}{-56}
=-1/7
$