4/9x+20=x

Solution for 4/9x+20=x equation:

4/9x+20=x

We move all terms to the left:

4/9x+20-(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+20=0

We multiply all the terms by the denominator


-1x*9x+20*9x+4=0

Wy multiply elements

-9x^2+180x+4=0

a = -9; b = 180; c = +4;
Δ = b2-4ac
Δ = 1802-4·(-9)·4
Δ = 32544
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:

$\sqrt{\Delta}=\sqrt{32544}=\sqrt{144*226}=\sqrt{144}*\sqrt{226}=12\sqrt{226}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-12\sqrt{226}}{2*-9}=\frac{-180-12\sqrt{226}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+12\sqrt{226}}{2*-9}=\frac{-180+12\sqrt{226}}{-18}
$