12x-8/2x-6=0

Solution for 12x-8/2x-6=0 equation:

12x-8/2x-6=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


12x*2x-6*2x-8=0

Wy multiply elements

24x^2-12x-8=0

a = 24; b = -12; c = -8;
Δ = b2-4ac
Δ = -122-4·24·(-8)
Δ = 912
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:

$\sqrt{\Delta}=\sqrt{912}=\sqrt{16*57}=\sqrt{16}*\sqrt{57}=4\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{57}}{2*24}=\frac{12-4\sqrt{57}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{57}}{2*24}=\frac{12+4\sqrt{57}}{48}
$