x/3x-4=7x+8

Solution for x/3x-4=7x+8 equation:

x/3x-4=7x+8

We move all terms to the left:

x/3x-4-(7x+8)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

x/3x-7x-8-4=0

We multiply all the terms by the denominator


x-7x*3x-8*3x-4*3x=0

Wy multiply elements

-21x^2+x-24x-12x=0

We add all the numbers together, and all the variables

-21x^2-35x=0

a = -21; b = -35; c = 0;
Δ = b2-4ac
Δ = -352-4·(-21)·0
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-35}{2*-21}=\frac{0}{-42}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+35}{2*-21}=\frac{70}{-42}
=-1+2/3
$