1/8x-1/2=3/4x+5

Solution for 1/8x-1/2=3/4x+5 equation:

1/8x-1/2=3/4x+5

We move all terms to the left:

1/8x-1/2-(3/4x+5)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 4x+5)!=0

x∈R


We get rid of parentheses

1/8x-3/4x-5-1/2=0

We calculate fractions


(-128x^2)/128x^2+16x/128x^2+(-96x)/128x^2-5=0

We multiply all the terms by the denominator


(-128x^2)+16x+(-96x)-5*128x^2=0

Wy multiply elements

(-128x^2)-640x^2+16x+(-96x)=0

We get rid of parentheses

-128x^2-640x^2+16x-96x=0

We add all the numbers together, and all the variables

-768x^2-80x=0

a = -768; b = -80; c = 0;
Δ = b2-4ac
Δ = -802-4·(-768)·0
Δ = 6400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6400}=80$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-80}{2*-768}=\frac{0}{-1536}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+80}{2*-768}=\frac{160}{-1536}
=-5/48
$