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

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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} $

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