4/3x-3/16=3/4x

Solution for 4/3x-3/16=3/4x equation:

4/3x-3/16=3/4x

We move all terms to the left:

4/3x-3/16-(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

4/3x-(+3/4x)-3/16=0

We get rid of parentheses

4/3x-3/4x-3/16=0

We calculate fractions


(-144x^2)/192x^2+256x/192x^2+(-144x)/192x^2=0

We multiply all the terms by the denominator


(-144x^2)+256x+(-144x)=0

We get rid of parentheses

-144x^2+256x-144x=0

We add all the numbers together, and all the variables

-144x^2+112x=0

a = -144; b = 112; c = 0;
Δ = b2-4ac
Δ = 1122-4·(-144)·0
Δ = 12544
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12544}=112$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(112)-112}{2*-144}=\frac{-224}{-288}
=7/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(112)+112}{2*-144}=\frac{0}{-288}
=0
$