3x-1+18/3x=29

Solution for 3x-1+18/3x=29 equation:

3x-1+18/3x=29

We move all terms to the left:

3x-1+18/3x-(29)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

3x+18/3x-30=0

We multiply all the terms by the denominator


3x*3x-30*3x+18=0

Wy multiply elements

9x^2-90x+18=0

a = 9; b = -90; c = +18;
Δ = b2-4ac
Δ = -902-4·9·18
Δ = 7452
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:

$\sqrt{\Delta}=\sqrt{7452}=\sqrt{324*23}=\sqrt{324}*\sqrt{23}=18\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-18\sqrt{23}}{2*9}=\frac{90-18\sqrt{23}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+18\sqrt{23}}{2*9}=\frac{90+18\sqrt{23}}{18}
$