2x-8/3x-6=0

Solution for 2x-8/3x-6=0 equation:

2x-8/3x-6=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


2x*3x-6*3x-8=0

Wy multiply elements

6x^2-18x-8=0

a = 6; b = -18; c = -8;
Δ = b2-4ac
Δ = -182-4·6·(-8)
Δ = 516
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:

$\sqrt{\Delta}=\sqrt{516}=\sqrt{4*129}=\sqrt{4}*\sqrt{129}=2\sqrt{129}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{129}}{2*6}=\frac{18-2\sqrt{129}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{129}}{2*6}=\frac{18+2\sqrt{129}}{12}
$