11-12x/3x+2-8x-8x-9/7-2x=0

Solution for 11-12x/3x+2-8x-8x-9/7-2x=0 equation:

11-12x/3x+2-8x-8x-9/7-2x=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-18x-12x/3x+13-9/7=0

We calculate fractions


-18x+(-84x)/21x+(-27x)/21x+13=0

We multiply all the terms by the denominator


-18x*21x+(-84x)+(-27x)+13*21x=0

Wy multiply elements

-378x^2+(-84x)+(-27x)+273x=0

We get rid of parentheses

-378x^2-84x-27x+273x=0

We add all the numbers together, and all the variables

-378x^2+162x=0

a = -378; b = 162; c = 0;
Δ = b2-4ac
Δ = 1622-4·(-378)·0
Δ = 26244
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{26244}=162$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(162)-162}{2*-378}=\frac{-324}{-756}
=3/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(162)+162}{2*-378}=\frac{0}{-756}
=0
$