6/2x-9-2/2x=x+1

Solution for 6/2x-9-2/2x=x+1 equation:

6/2x-9-2/2x=x+1

We move all terms to the left:

6/2x-9-2/2x-(x+1)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

6/2x-2/2x-x-1-9=0

We multiply all the terms by the denominator


-x*2x-1*2x-9*2x+6-2=0

We add all the numbers together, and all the variables

-x*2x-1*2x-9*2x+4=0

Wy multiply elements

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

We add all the numbers together, and all the variables

-2x^2-20x+4=0

a = -2; b = -20; c = +4;
Δ = b2-4ac
Δ = -202-4·(-2)·4
Δ = 432
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:

$\sqrt{\Delta}=\sqrt{432}=\sqrt{144*3}=\sqrt{144}*\sqrt{3}=12\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-12\sqrt{3}}{2*-2}=\frac{20-12\sqrt{3}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+12\sqrt{3}}{2*-2}=\frac{20+12\sqrt{3}}{-4}
$