3/9x-4x=3

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

3/9x-4x=3

We move all terms to the left:

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


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We add all the numbers together, and all the variables

-4x+3/9x-3=0

We multiply all the terms by the denominator


-4x*9x-3*9x+3=0

Wy multiply elements

-36x^2-27x+3=0

a = -36; b = -27; c = +3;
Δ = b2-4ac
Δ = -272-4·(-36)·3
Δ = 1161
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1161}=\sqrt{9*129}=\sqrt{9}*\sqrt{129}=3\sqrt{129}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-3\sqrt{129}}{2*-36}=\frac{27-3\sqrt{129}}{-72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+3\sqrt{129}}{2*-36}=\frac{27+3\sqrt{129}}{-72}
$