3x(x-4)/x-0=0

Solution for 3x(x-4)/x-0=0 equation:

3x(x-4)/x-0=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

3x(x-4)/x=0

We multiply all the terms by the denominator


3x(x-4)=0

We multiply parentheses

3x^2-12x=0

a = 3; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·3·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12}{2*3}=\frac{0}{6}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*3}=\frac{24}{6}
=4
$