3x(x-5)=12x

Solution for 3x(x-5)=12x equation:

3x(x-5)=12x

We move all terms to the left:

3x(x-5)-(12x)=0

We add all the numbers together, and all the variables

-12x+3x(x-5)=0

We multiply parentheses

3x^2-12x-15x=0

We add all the numbers together, and all the variables

3x^2-27x=0

a = 3; b = -27; c = 0;
Δ = b2-4ac
Δ = -272-4·3·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-27}{2*3}=\frac{0}{6}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+27}{2*3}=\frac{54}{6}
=9
$