1/4x+1/8x-1+2/4=85/8

Solution for 1/4x+1/8x-1+2/4=85/8 equation:

1/4x+1/8x-1+2/4=85/8

We move all terms to the left:

1/4x+1/8x-1+2/4-(85/8)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

1/4x+1/8x-1+2/4-(+85/8)=0

We get rid of parentheses

1/4x+1/8x-1+2/4-85/8=0

We calculate fractions


512x/4096x^2+64x/4096x^2+1024x/4096x^2+(-5440x)/4096x^2-1=0

We multiply all the terms by the denominator


512x+64x+1024x+(-5440x)-1*4096x^2=0

We add all the numbers together, and all the variables

1600x+(-5440x)-1*4096x^2=0

Wy multiply elements

-4096x^2+1600x+(-5440x)=0

We get rid of parentheses

-4096x^2+1600x-5440x=0

We add all the numbers together, and all the variables

-4096x^2-3840x=0

a = -4096; b = -3840; c = 0;
Δ = b2-4ac
Δ = -38402-4·(-4096)·0
Δ = 14745600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{14745600}=3840$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3840)-3840}{2*-4096}=\frac{0}{-8192}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3840)+3840}{2*-4096}=\frac{7680}{-8192}
=-15/16
$