X+4/9x=104

Solution for X+4/9x=104 equation:

X+4/9X=104

We move all terms to the left:

X+4/9X-(104)=0


Domain of the equation: 9X!=0

X!=0/9

X!=0

X∈R


We multiply all the terms by the denominator


X*9X-104*9X+4=0

Wy multiply elements

9X^2-936X+4=0

a = 9; b = -936; c = +4;
Δ = b2-4ac
Δ = -9362-4·9·4
Δ = 875952
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:

$\sqrt{\Delta}=\sqrt{875952}=\sqrt{144*6083}=\sqrt{144}*\sqrt{6083}=12\sqrt{6083}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-936)-12\sqrt{6083}}{2*9}=\frac{936-12\sqrt{6083}}{18}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-936)+12\sqrt{6083}}{2*9}=\frac{936+12\sqrt{6083}}{18}
$