1/2x+1/4x+1/8=35/8

Solution for 1/2x+1/4x+1/8=35/8 equation:

1/2x+1/4x+1/8=35/8

We move all terms to the left:

1/2x+1/4x+1/8-(35/8)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x+1/4x+1/8-(+35/8)=0

We get rid of parentheses

1/2x+1/4x+1/8-35/8=0

We calculate fractions


(-1120x^2+1)/512x^2+256x/512x^2+128x/512x^2=0

We multiply all the terms by the denominator


(-1120x^2+1)+256x+128x=0

We add all the numbers together, and all the variables

(-1120x^2+1)+384x=0

We get rid of parentheses

-1120x^2+384x+1=0

a = -1120; b = 384; c = +1;
Δ = b2-4ac
Δ = 3842-4·(-1120)·1
Δ = 151936
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:

$\sqrt{\Delta}=\sqrt{151936}=\sqrt{64*2374}=\sqrt{64}*\sqrt{2374}=8\sqrt{2374}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(384)-8\sqrt{2374}}{2*-1120}=\frac{-384-8\sqrt{2374}}{-2240}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(384)+8\sqrt{2374}}{2*-1120}=\frac{-384+8\sqrt{2374}}{-2240}
$