3/9x+5/9x=x

Solution for 3/9x+5/9x=x equation:

3/9x+5/9x=x

We move all terms to the left:

3/9x+5/9x-(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

-1x+3/9x+5/9x=0

We multiply all the terms by the denominator


-1x*9x+3+5=0

We add all the numbers together, and all the variables

-1x*9x+8=0

Wy multiply elements

-9x^2+8=0

a = -9; b = 0; c = +8;
Δ = b2-4ac
Δ = 02-4·(-9)·8
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{2}}{2*-9}=\frac{0-12\sqrt{2}}{-18}
=-\frac{12\sqrt{2}}{-18}
=-\frac{2\sqrt{2}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{2}}{2*-9}=\frac{0+12\sqrt{2}}{-18}
=\frac{12\sqrt{2}}{-18}
=\frac{2\sqrt{2}}{-3}
$