5/4x-1/2x=-1/8-35

Solution for 5/4x-1/2x=-1/8-35 equation:

5/4x-1/2x=-1/8-35

We move all terms to the left:

5/4x-1/2x-(-1/8-35)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

5/4x-1/2x+35+1/8=0

We calculate fractions


16x^2/512x^2+640x/512x^2+(-256x)/512x^2+35=0

We multiply all the terms by the denominator


16x^2+640x+(-256x)+35*512x^2=0

Wy multiply elements

16x^2+17920x^2+640x+(-256x)=0

We get rid of parentheses

16x^2+17920x^2+640x-256x=0

We add all the numbers together, and all the variables

17936x^2+384x=0

a = 17936; b = 384; c = 0;
Δ = b2-4ac
Δ = 3842-4·17936·0
Δ = 147456
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{147456}=384$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(384)-384}{2*17936}=\frac{-768}{35872}
=-24/1121
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(384)+384}{2*17936}=\frac{0}{35872}
=0
$