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

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

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

We move all terms to the left:

3/4x+5-(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+5=0

We calculate fractions


24x/32x^2+(-4x)/32x^2+1+5=0

We add all the numbers together, and all the variables

24x/32x^2+(-4x)/32x^2+6=0

We multiply all the terms by the denominator


24x+(-4x)+6*32x^2=0

Wy multiply elements

192x^2+24x+(-4x)=0

We get rid of parentheses

192x^2+24x-4x=0

We add all the numbers together, and all the variables

192x^2+20x=0

a = 192; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·192·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20}{2*192}=\frac{-40}{384}
=-5/48
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*192}=\frac{0}{384}
=0
$