x-6/8x=16

Solution for x-6/8x=16 equation:

x-6/8x=16

We move all terms to the left:

x-6/8x-(16)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We multiply all the terms by the denominator


x*8x-16*8x-6=0

Wy multiply elements

8x^2-128x-6=0

a = 8; b = -128; c = -6;
Δ = b2-4ac
Δ = -1282-4·8·(-6)
Δ = 16576
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:

$\sqrt{\Delta}=\sqrt{16576}=\sqrt{64*259}=\sqrt{64}*\sqrt{259}=8\sqrt{259}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-128)-8\sqrt{259}}{2*8}=\frac{128-8\sqrt{259}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-128)+8\sqrt{259}}{2*8}=\frac{128+8\sqrt{259}}{16}
$