10/8x-2/4x=2

Solution for 10/8x-2/4x=2 equation:

10/8x-2/4x=2

We move all terms to the left:

10/8x-2/4x-(2)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We calculate fractions


40x/32x^2+(-16x)/32x^2-2=0

We multiply all the terms by the denominator


40x+(-16x)-2*32x^2=0

Wy multiply elements

-64x^2+40x+(-16x)=0

We get rid of parentheses

-64x^2+40x-16x=0

We add all the numbers together, and all the variables

-64x^2+24x=0

a = -64; b = 24; c = 0;
Δ = b2-4ac
Δ = 242-4·(-64)·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-24}{2*-64}=\frac{-48}{-128}
=3/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+24}{2*-64}=\frac{0}{-128}
=0
$