4/9x=9+3x

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

4/9x=9+3x

We move all terms to the left:

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


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

4/9x-3x-9=0

We multiply all the terms by the denominator


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

Wy multiply elements

-27x^2-81x+4=0

a = -27; b = -81; c = +4;
Δ = b2-4ac
Δ = -812-4·(-27)·4
Δ = 6993
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:

$\sqrt{\Delta}=\sqrt{6993}=\sqrt{9*777}=\sqrt{9}*\sqrt{777}=3\sqrt{777}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-81)-3\sqrt{777}}{2*-27}=\frac{81-3\sqrt{777}}{-54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-81)+3\sqrt{777}}{2*-27}=\frac{81+3\sqrt{777}}{-54}
$