-4/9x-3/4x=16/27

Solution for -4/9x-3/4x=16/27 equation:

-4/9x-3/4x=16/27

We move all terms to the left:

-4/9x-3/4x-(16/27)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

-4/9x-3/4x-(+16/27)=0

We get rid of parentheses

-4/9x-3/4x-16/27=0

We calculate fractions


(-2304x^2)/1944x^2+(-864x)/1944x^2+(-1458x)/1944x^2=0

We multiply all the terms by the denominator


(-2304x^2)+(-864x)+(-1458x)=0

We get rid of parentheses

-2304x^2-864x-1458x=0

We add all the numbers together, and all the variables

-2304x^2-2322x=0

a = -2304; b = -2322; c = 0;
Δ = b2-4ac
Δ = -23222-4·(-2304)·0
Δ = 5391684
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5391684}=2322$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2322)-2322}{2*-2304}=\frac{0}{-4608}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2322)+2322}{2*-2304}=\frac{4644}{-4608}
=-1+1/128
$