3/4x+5=1/8x-6

Solution for 3/4x+5=1/8x-6 equation:

3/4x+5=1/8x-6

We move all terms to the left:

3/4x+5-(1/8x-6)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 8x-6)!=0

x∈R


We get rid of parentheses

3/4x-1/8x+6+5=0

We calculate fractions


24x/32x^2+(-4x)/32x^2+6+5=0

We add all the numbers together, and all the variables

24x/32x^2+(-4x)/32x^2+11=0

We multiply all the terms by the denominator


24x+(-4x)+11*32x^2=0

Wy multiply elements

352x^2+24x+(-4x)=0

We get rid of parentheses

352x^2+24x-4x=0

We add all the numbers together, and all the variables

352x^2+20x=0

a = 352; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·352·0
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*352}=\frac{-40}{704}
=-5/88
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*352}=\frac{0}{704}
=0
$