9x+1/3x=38

Solution for 9x+1/3x=38 equation:

9x+1/3x=38

We move all terms to the left:

9x+1/3x-(38)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


9x*3x-38*3x+1=0

Wy multiply elements

27x^2-114x+1=0

a = 27; b = -114; c = +1;
Δ = b2-4ac
Δ = -1142-4·27·1
Δ = 12888
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:

$\sqrt{\Delta}=\sqrt{12888}=\sqrt{36*358}=\sqrt{36}*\sqrt{358}=6\sqrt{358}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-114)-6\sqrt{358}}{2*27}=\frac{114-6\sqrt{358}}{54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-114)+6\sqrt{358}}{2*27}=\frac{114+6\sqrt{358}}{54}
$