4/3x-13=x-9

Solution for 4/3x-13=x-9 equation:

4/3x-13=x-9

We move all terms to the left:

4/3x-13-(x-9)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

4/3x-x+9-13=0

We multiply all the terms by the denominator


-x*3x+9*3x-13*3x+4=0

Wy multiply elements

-3x^2+27x-39x+4=0

We add all the numbers together, and all the variables

-3x^2-12x+4=0

a = -3; b = -12; c = +4;
Δ = b2-4ac
Δ = -122-4·(-3)·4
Δ = 192
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:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-8\sqrt{3}}{2*-3}=\frac{12-8\sqrt{3}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+8\sqrt{3}}{2*-3}=\frac{12+8\sqrt{3}}{-6}
$