1/3x-9=14x-1-13x

Solution for 1/3x-9=14x-1-13x equation:

1/3x-9=14x-1-13x

We move all terms to the left:

1/3x-9-(14x-1-13x)=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-(x-1)-9=0

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

-3x^2-24x+1=0

a = -3; b = -24; c = +1;
Δ = b2-4ac
Δ = -242-4·(-3)·1
Δ = 588
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:

$\sqrt{\Delta}=\sqrt{588}=\sqrt{196*3}=\sqrt{196}*\sqrt{3}=14\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-14\sqrt{3}}{2*-3}=\frac{24-14\sqrt{3}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+14\sqrt{3}}{2*-3}=\frac{24+14\sqrt{3}}{-6}
$