-5/12x-1=-3/4x-9=

Solution for -5/12x-1=-3/4x-9= equation:

-5/12x-1=-3/4x-9=

We move all terms to the left:

-5/12x-1-(-3/4x-9)=0


Domain of the equation: 12x!=0

x!=0/12

x!=0

x∈R



Domain of the equation: 4x-9)!=0

x∈R


We get rid of parentheses

-5/12x+3/4x+9-1=0

We calculate fractions


(-20x)/48x^2+36x/48x^2+9-1=0

We add all the numbers together, and all the variables

(-20x)/48x^2+36x/48x^2+8=0

We multiply all the terms by the denominator


(-20x)+36x+8*48x^2=0

We add all the numbers together, and all the variables

36x+(-20x)+8*48x^2=0

Wy multiply elements

384x^2+36x+(-20x)=0

We get rid of parentheses

384x^2+36x-20x=0

We add all the numbers together, and all the variables

384x^2+16x=0

a = 384; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·384·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-16}{2*384}=\frac{-32}{768}
=-1/24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+16}{2*384}=\frac{0}{768}
=0
$