((5)x-1)/6)-x=1-x/9

Solution for ((5)x-1)/6)-x=1-x/9 equation:

((5)x-1)/6)-x=1-x/9

We move all terms to the left:

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


Domain of the equation: 6)-x-(1!=0

x∈R


We add all the numbers together, and all the variables

(5x-1)/6)-x-(-x/9+1)=0

We add all the numbers together, and all the variables

(5x-1)/6)-x-(-x/9=0

We calculate fractions


(-6x^2)/6+(45x-9)/6-x-x-(*9)-(*9)=0

We add all the numbers together, and all the variables

(-6x^2)/6+(45x-9)/6-x-x-0-0=0

We add all the numbers together, and all the variables

(-6x^2)/6-2x+(45x-9)/6=0

We multiply all the terms by the denominator


(-6x^2)-2x*6+(45x-9)=0

Wy multiply elements

(-6x^2)-12x+(45x-9)=0

We get rid of parentheses

-6x^2-12x+45x-9=0

We add all the numbers together, and all the variables

-6x^2+33x-9=0

a = -6; b = 33; c = -9;
Δ = b2-4ac
Δ = 332-4·(-6)·(-9)
Δ = 873
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:

$\sqrt{\Delta}=\sqrt{873}=\sqrt{9*97}=\sqrt{9}*\sqrt{97}=3\sqrt{97}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-3\sqrt{97}}{2*-6}=\frac{-33-3\sqrt{97}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+3\sqrt{97}}{2*-6}=\frac{-33+3\sqrt{97}}{-12}
$