3x+4/9x-8=x

Solution for 3x+4/9x-8=x equation:

3x+4/9x-8=x

We move all terms to the left:

3x+4/9x-8-(x)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We add all the numbers together, and all the variables

2x+4/9x-8=0

We multiply all the terms by the denominator


2x*9x-8*9x+4=0

Wy multiply elements

18x^2-72x+4=0

a = 18; b = -72; c = +4;
Δ = b2-4ac
Δ = -722-4·18·4
Δ = 4896
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:

$\sqrt{\Delta}=\sqrt{4896}=\sqrt{144*34}=\sqrt{144}*\sqrt{34}=12\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-12\sqrt{34}}{2*18}=\frac{72-12\sqrt{34}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+12\sqrt{34}}{2*18}=\frac{72+12\sqrt{34}}{36}
$