-12/3x-31/4x=-111/16

Solution for -12/3x-31/4x=-111/16 equation:

-12/3x-31/4x=-111/16

We move all terms to the left:

-12/3x-31/4x-(-111/16)=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 get rid of parentheses

-12/3x-31/4x+111/16=0

We calculate fractions


5328x^2/192x^2+(-768x)/192x^2+(-1488x)/192x^2=0

We multiply all the terms by the denominator


5328x^2+(-768x)+(-1488x)=0

We get rid of parentheses

5328x^2-768x-1488x=0

We add all the numbers together, and all the variables

5328x^2-2256x=0

a = 5328; b = -2256; c = 0;
Δ = b2-4ac
Δ = -22562-4·5328·0
Δ = 5089536
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5089536}=2256$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2256)-2256}{2*5328}=\frac{0}{10656}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2256)+2256}{2*5328}=\frac{4512}{10656}
=47/111
$