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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 8x+1)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


(-256x^2)/128x^2+96x/128x^2+(-16x)/128x^2-1=0

We multiply all the terms by the denominator


(-256x^2)+96x+(-16x)-1*128x^2=0

Wy multiply elements

(-256x^2)-128x^2+96x+(-16x)=0

We get rid of parentheses

-256x^2-128x^2+96x-16x=0

We add all the numbers together, and all the variables

-384x^2+80x=0

a = -384; b = 80; c = 0;
Δ = b2-4ac
Δ = 802-4·(-384)·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*-384}=\frac{-160}{-768}
=5/24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+80}{2*-384}=\frac{0}{-768}
=0
$