x(x-3)=6x

Solution for x(x-3)=6x equation:

x(x-3)=6x

We move all terms to the left:

x(x-3)-(6x)=0

We add all the numbers together, and all the variables

-6x+x(x-3)=0

We multiply parentheses

x^2-6x-3x=0

We add all the numbers together, and all the variables

x^2-9x=0

a = 1; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·1·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*1}=\frac{0}{2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*1}=\frac{18}{2}
=9
$