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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-36x^2)/96x^2+32x/96x^2+(-48x)/96x^2-2=0

We multiply all the terms by the denominator


(-36x^2)+32x+(-48x)-2*96x^2=0

Wy multiply elements

(-36x^2)-192x^2+32x+(-48x)=0

We get rid of parentheses

-36x^2-192x^2+32x-48x=0

We add all the numbers together, and all the variables

-228x^2-16x=0

a = -228; b = -16; c = 0;
Δ = b2-4ac
Δ = -162-4·(-228)·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*-228}=\frac{0}{-456}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16}{2*-228}=\frac{32}{-456}
=-4/57
$