x/8x-2=4x+6

Solution for x/8x-2=4x+6 equation:

x/8x-2=4x+6

We move all terms to the left:

x/8x-2-(4x+6)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We get rid of parentheses

x/8x-4x-6-2=0

We multiply all the terms by the denominator


x-4x*8x-6*8x-2*8x=0

Wy multiply elements

-32x^2+x-48x-16x=0

We add all the numbers together, and all the variables

-32x^2-63x=0

a = -32; b = -63; c = 0;
Δ = b2-4ac
Δ = -632-4·(-32)·0
Δ = 3969
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3969}=63$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-63)-63}{2*-32}=\frac{0}{-64}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-63)+63}{2*-32}=\frac{126}{-64}
=-1+31/32
$