x/8x+4=3x-6

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

x/8x+4=3x-6

We move all terms to the left:

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


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


x-3x*8x+6*8x+4*8x=0

Wy multiply elements

-24x^2+x+48x+32x=0

We add all the numbers together, and all the variables

-24x^2+81x=0

a = -24; b = 81; c = 0;
Δ = b2-4ac
Δ = 812-4·(-24)·0
Δ = 6561
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6561}=81$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(81)-81}{2*-24}=\frac{-162}{-48}
=3+3/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(81)+81}{2*-24}=\frac{0}{-48}
=0
$