4/9x-5=x

Solution for 4/9x-5=x equation:

4/9x-5=x

We move all terms to the left:

4/9x-5-(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+4/9x-5=0

We multiply all the terms by the denominator


-1x*9x-5*9x+4=0

Wy multiply elements

-9x^2-45x+4=0

a = -9; b = -45; c = +4;
Δ = b2-4ac
Δ = -452-4·(-9)·4
Δ = 2169
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:

$\sqrt{\Delta}=\sqrt{2169}=\sqrt{9*241}=\sqrt{9}*\sqrt{241}=3\sqrt{241}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-3\sqrt{241}}{2*-9}=\frac{45-3\sqrt{241}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+3\sqrt{241}}{2*-9}=\frac{45+3\sqrt{241}}{-18}
$