x-4/3x-5=-2

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Solution for x-4/3x-5=-2 equation: 



x-4/3x-5=-2

We move all terms to the left:

x-4/3x-5-(-2)=0



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



We add all the numbers together, and all the variables

x-4/3x-3=0

We multiply all the terms by the denominator


x*3x-3*3x-4=0

Wy multiply elements

3x^2-9x-4=0

a = 3; b = -9; c = -4;
Δ = b2-4ac
Δ = -92-4·3·(-4)
Δ = 129
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{129}}{2*3}=\frac{9-\sqrt{129}}{6}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{129}}{2*3}=\frac{9+\sqrt{129}}{6}
$

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