X+1/9x=4

Solution for X+1/9x=4 equation:

X+1/9X=4

We move all terms to the left:

X+1/9X-(4)=0


Domain of the equation: 9X!=0

X!=0/9

X!=0

X∈R


We multiply all the terms by the denominator


X*9X-4*9X+1=0

Wy multiply elements

9X^2-36X+1=0

a = 9; b = -36; c = +1;
Δ = b2-4ac
Δ = -362-4·9·1
Δ = 1260
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:

$\sqrt{\Delta}=\sqrt{1260}=\sqrt{36*35}=\sqrt{36}*\sqrt{35}=6\sqrt{35}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-6\sqrt{35}}{2*9}=\frac{36-6\sqrt{35}}{18}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+6\sqrt{35}}{2*9}=\frac{36+6\sqrt{35}}{18}
$