40+1/9x=x

Solution for 40+1/9x=x equation:

40+1/9x=x

We move all terms to the left:

40+1/9x-(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+1/9x+40=0

We multiply all the terms by the denominator


-1x*9x+40*9x+1=0

Wy multiply elements

-9x^2+360x+1=0

a = -9; b = 360; c = +1;
Δ = b2-4ac
Δ = 3602-4·(-9)·1
Δ = 129636
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:

$\sqrt{\Delta}=\sqrt{129636}=\sqrt{36*3601}=\sqrt{36}*\sqrt{3601}=6\sqrt{3601}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(360)-6\sqrt{3601}}{2*-9}=\frac{-360-6\sqrt{3601}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(360)+6\sqrt{3601}}{2*-9}=\frac{-360+6\sqrt{3601}}{-18}
$