2x-5/3x-8=1

Solution for 2x-5/3x-8=1 equation:

2x-5/3x-8=1

We move all terms to the left:

2x-5/3x-8-(1)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

2x-5/3x-9=0

We multiply all the terms by the denominator


2x*3x-9*3x-5=0

Wy multiply elements

6x^2-27x-5=0

a = 6; b = -27; c = -5;
Δ = b2-4ac
Δ = -272-4·6·(-5)
Δ = 849
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{-(-27)-\sqrt{849}}{2*6}=\frac{27-\sqrt{849}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+\sqrt{849}}{2*6}=\frac{27+\sqrt{849}}{12}
$