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

Solution for x(3x+8)/(3x-8)=0 equation:

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


Domain of the equation: (3x-8)!=0

We move all terms containing x to the left, all other terms to the right

3x!=8

x!=8/3

x!=2+2/3

x∈R


We multiply all the terms by the denominator


x(3x+8)=0

We multiply parentheses

3x^2+8x=0

a = 3; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·3·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*3}=\frac{-16}{6}
=-2+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*3}=\frac{0}{6}
=0
$