3x-16/8x-14=0

Solution for 3x-16/8x-14=0 equation:

3x-16/8x-14=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We multiply all the terms by the denominator


3x*8x-14*8x-16=0

Wy multiply elements

24x^2-112x-16=0

a = 24; b = -112; c = -16;
Δ = b2-4ac
Δ = -1122-4·24·(-16)
Δ = 14080
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:

$\sqrt{\Delta}=\sqrt{14080}=\sqrt{256*55}=\sqrt{256}*\sqrt{55}=16\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-112)-16\sqrt{55}}{2*24}=\frac{112-16\sqrt{55}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-112)+16\sqrt{55}}{2*24}=\frac{112+16\sqrt{55}}{48}
$