6/x-6=-5/2x-12+2

Solution for 6/x-6=-5/2x-12+2 equation:

6/x-6=-5/2x-12+2

We move all terms to the left:

6/x-6-(-5/2x-12+2)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x-12+2)!=0

We move all terms containing x to the left, all other terms to the right

2x+2)!=12

x∈R


We add all the numbers together, and all the variables

6/x-(-5/2x-10)-6=0

We get rid of parentheses

6/x+5/2x+10-6=0

We calculate fractions


12x/2x^2+5x/2x^2+10-6=0

We add all the numbers together, and all the variables

12x/2x^2+5x/2x^2+4=0

We multiply all the terms by the denominator


12x+5x+4*2x^2=0

We add all the numbers together, and all the variables

17x+4*2x^2=0

Wy multiply elements

8x^2+17x=0

a = 8; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·8·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*8}=\frac{-34}{16}
=-2+1/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*8}=\frac{0}{16}
=0
$