5/3x-9=1x-6

Solution for 5/3x-9=1x-6 equation:

5/3x-9=1x-6

We move all terms to the left:

5/3x-9-(1x-6)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

5/3x-(x-6)-9=0

We get rid of parentheses

5/3x-x+6-9=0

We multiply all the terms by the denominator


-x*3x+6*3x-9*3x+5=0

Wy multiply elements

-3x^2+18x-27x+5=0

We add all the numbers together, and all the variables

-3x^2-9x+5=0

a = -3; b = -9; c = +5;
Δ = b2-4ac
Δ = -92-4·(-3)·5
Δ = 141
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{141}}{2*-3}=\frac{9-\sqrt{141}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{141}}{2*-3}=\frac{9+\sqrt{141}}{-6}
$