1/3x-1/2x=11/4

Solution for 1/3x-1/2x=11/4 equation:

1/3x-1/2x=11/4

We move all terms to the left:

1/3x-1/2x-(11/4)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

1/3x-1/2x-(+11/4)=0

We get rid of parentheses

1/3x-1/2x-11/4=0

We calculate fractions


(-132x^2)/96x^2+32x/96x^2+(-48x)/96x^2=0

We multiply all the terms by the denominator


(-132x^2)+32x+(-48x)=0

We get rid of parentheses

-132x^2+32x-48x=0

We add all the numbers together, and all the variables

-132x^2-16x=0

a = -132; b = -16; c = 0;
Δ = b2-4ac
Δ = -162-4·(-132)·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*-132}=\frac{0}{-264}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16}{2*-132}=\frac{32}{-264}
=-4/33
$