9-1/3x=1-6x

Solution for 9-1/3x=1-6x equation:

9-1/3x=1-6x

We move all terms to the left:

9-1/3x-(1-6x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-1/3x-(-6x+1)+9=0

We get rid of parentheses

-1/3x+6x-1+9=0

We multiply all the terms by the denominator


6x*3x-1*3x+9*3x-1=0

Wy multiply elements

18x^2-3x+27x-1=0

We add all the numbers together, and all the variables

18x^2+24x-1=0

a = 18; b = 24; c = -1;
Δ = b2-4ac
Δ = 242-4·18·(-1)
Δ = 648
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:

$\sqrt{\Delta}=\sqrt{648}=\sqrt{324*2}=\sqrt{324}*\sqrt{2}=18\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-18\sqrt{2}}{2*18}=\frac{-24-18\sqrt{2}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+18\sqrt{2}}{2*18}=\frac{-24+18\sqrt{2}}{36}
$