8x-6/24x-32=0

Solution for 8x-6/24x-32=0 equation:

8x-6/24x-32=0


Domain of the equation: 24x!=0

x!=0/24

x!=0

x∈R


We multiply all the terms by the denominator


8x*24x-32*24x-6=0

Wy multiply elements

192x^2-768x-6=0

a = 192; b = -768; c = -6;
Δ = b2-4ac
Δ = -7682-4·192·(-6)
Δ = 594432
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:

$\sqrt{\Delta}=\sqrt{594432}=\sqrt{2304*258}=\sqrt{2304}*\sqrt{258}=48\sqrt{258}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-768)-48\sqrt{258}}{2*192}=\frac{768-48\sqrt{258}}{384}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-768)+48\sqrt{258}}{2*192}=\frac{768+48\sqrt{258}}{384}
$