-1/2x-12+1=4/x-6

Solution for -1/2x-12+1=4/x-6 equation:

-1/2x-12+1=4/x-6

We move all terms to the left:

-1/2x-12+1-(4/x-6)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: x-6)!=0

x∈R


We add all the numbers together, and all the variables

-1/2x-(4/x-6)-11=0

We get rid of parentheses

-1/2x-4/x+6-11=0

We calculate fractions


(-x)/2x^2+(-8x)/2x^2+6-11=0

We add all the numbers together, and all the variables

(-1x)/2x^2+(-8x)/2x^2+6-11=0

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-10x^2+(-1x)+(-8x)=0

We get rid of parentheses

-10x^2-1x-8x=0

We add all the numbers together, and all the variables

-10x^2-9x=0

a = -10; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·(-10)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*-10}=\frac{0}{-20}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*-10}=\frac{18}{-20}
=-9/10
$