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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 8x+4)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


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

We add all the numbers together, and all the variables

24x/32x^2+(-4x)/32x^2-10=0

We multiply all the terms by the denominator


24x+(-4x)-10*32x^2=0

Wy multiply elements

-320x^2+24x+(-4x)=0

We get rid of parentheses

-320x^2+24x-4x=0

We add all the numbers together, and all the variables

-320x^2+20x=0

a = -320; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·(-320)·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*-320}=\frac{-40}{-640}
=1/16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*-320}=\frac{0}{-640}
=0
$