9x-1/3x+1=26

Solution for 9x-1/3x+1=26 equation:

9x-1/3x+1=26

We move all terms to the left:

9x-1/3x+1-(26)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

9x-1/3x-25=0

We multiply all the terms by the denominator


9x*3x-25*3x-1=0

Wy multiply elements

27x^2-75x-1=0

a = 27; b = -75; c = -1;
Δ = b2-4ac
Δ = -752-4·27·(-1)
Δ = 5733
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:

$\sqrt{\Delta}=\sqrt{5733}=\sqrt{441*13}=\sqrt{441}*\sqrt{13}=21\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-75)-21\sqrt{13}}{2*27}=\frac{75-21\sqrt{13}}{54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+21\sqrt{13}}{2*27}=\frac{75+21\sqrt{13}}{54}
$