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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

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

We calculate fractions


54x^2/96x^2+48x/96x^2+(-64x)/96x^2=0

We multiply all the terms by the denominator


54x^2+48x+(-64x)=0

We get rid of parentheses

54x^2+48x-64x=0

We add all the numbers together, and all the variables

54x^2-16x=0

a = 54; b = -16; c = 0;
Δ = b2-4ac
Δ = -162-4·54·0
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*54}=\frac{0}{108}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16}{2*54}=\frac{32}{108}
=8/27
$