9/3x-1/2=3/4x

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Solution for 9/3x-1/2=3/4x equation: 



9/3x-1/2=3/4x

We move all terms to the left:

9/3x-1/2-(3/4x)=0



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R





Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R



We add all the numbers together, and all the variables

9/3x-(+3/4x)-1/2=0

We get rid of parentheses

9/3x-3/4x-1/2=0

We calculate fractions


(-48x^2)/48x^2+144x/48x^2+(-36x)/48x^2=0

We multiply all the terms by the denominator


(-48x^2)+144x+(-36x)=0

We get rid of parentheses

-48x^2+144x-36x=0

We add all the numbers together, and all the variables

-48x^2+108x=0

a = -48; b = 108; c = 0;
Δ = b2-4ac
Δ = 1082-4·(-48)·0
Δ = 11664
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{11664}=108$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(108)-108}{2*-48}=\frac{-216}{-96}
=2+1/4
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(108)+108}{2*-48}=\frac{0}{-96}
=0
$

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