-3/4x-9=-6-8/12x

Solution for -3/4x-9=-6-8/12x equation:

-3/4x-9=-6-8/12x

We move all terms to the left:

-3/4x-9-(-6-8/12x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 12x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-3/4x-(-8/12x-6)-9=0

We get rid of parentheses

-3/4x+8/12x+6-9=0

We calculate fractions


(-36x)/48x^2+32x/48x^2+6-9=0

We add all the numbers together, and all the variables

(-36x)/48x^2+32x/48x^2-3=0

We multiply all the terms by the denominator


(-36x)+32x-3*48x^2=0

We add all the numbers together, and all the variables

32x+(-36x)-3*48x^2=0

Wy multiply elements

-144x^2+32x+(-36x)=0

We get rid of parentheses

-144x^2+32x-36x=0

We add all the numbers together, and all the variables

-144x^2-4x=0

a = -144; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-144)·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*-144}=\frac{0}{-288}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-144}=\frac{8}{-288}
=-1/36
$