5/4x-3/6=12/3x

Solution for 5/4x-3/6=12/3x equation:

5/4x-3/6=12/3x

We move all terms to the left:

5/4x-3/6-(12/3x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5/4x-(+12/3x)-3/6=0

We get rid of parentheses

5/4x-12/3x-3/6=0

We calculate fractions


(-108x^2)/432x^2+540x/432x^2+(-1728x)/432x^2=0

We multiply all the terms by the denominator


(-108x^2)+540x+(-1728x)=0

We get rid of parentheses

-108x^2+540x-1728x=0

We add all the numbers together, and all the variables

-108x^2-1188x=0

a = -108; b = -1188; c = 0;
Δ = b2-4ac
Δ = -11882-4·(-108)·0
Δ = 1411344
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1411344}=1188$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1188)-1188}{2*-108}=\frac{0}{-216}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1188)+1188}{2*-108}=\frac{2376}{-216}
=-11
$