x+1/9x=40

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

x+1/9x=40

We move all terms to the left:

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


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We multiply all the terms by the denominator


x*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 = 129564
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:

$\sqrt{\Delta}=\sqrt{129564}=\sqrt{36*3599}=\sqrt{36}*\sqrt{3599}=6\sqrt{3599}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-360)-6\sqrt{3599}}{2*9}=\frac{360-6\sqrt{3599}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-360)+6\sqrt{3599}}{2*9}=\frac{360+6\sqrt{3599}}{18}
$