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

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

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

We move all terms to the left:

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


Domain of the equation: 3)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

4x^2-(x-9)-13=0

We get rid of parentheses

4x^2-x+9-13=0

We add all the numbers together, and all the variables

4x^2-1x-4=0

a = 4; b = -1; c = -4;
Δ = b2-4ac
Δ = -12-4·4·(-4)
Δ = 65
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{-(-1)-\sqrt{65}}{2*4}=\frac{1-\sqrt{65}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{65}}{2*4}=\frac{1+\sqrt{65}}{8}
$