-12/3x-31/4x=-11/1

Solution for -12/3x-31/4x=-11/1 equation:

-12/3x-31/4x=-11/1

We move all terms to the left:

-12/3x-31/4x-(-11/1)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

-12/3x-31/4x-(-11)=0

We add all the numbers together, and all the variables

-12/3x-31/4x+11=0

We calculate fractions


(-48x)/12x^2+(-93x)/12x^2+11=0

We multiply all the terms by the denominator


(-48x)+(-93x)+11*12x^2=0

Wy multiply elements

132x^2+(-48x)+(-93x)=0

We get rid of parentheses

132x^2-48x-93x=0

We add all the numbers together, and all the variables

132x^2-141x=0

a = 132; b = -141; c = 0;
Δ = b2-4ac
Δ = -1412-4·132·0
Δ = 19881
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{19881}=141$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-141)-141}{2*132}=\frac{0}{264}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-141)+141}{2*132}=\frac{282}{264}
=1+3/44
$