9x(x-2)=3x

Solution for 9x(x-2)=3x equation:

9x(x-2)=3x

We move all terms to the left:

9x(x-2)-(3x)=0

We add all the numbers together, and all the variables

-3x+9x(x-2)=0

We multiply parentheses

9x^2-3x-18x=0

We add all the numbers together, and all the variables

9x^2-21x=0

a = 9; b = -21; c = 0;
Δ = b2-4ac
Δ = -212-4·9·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-21}{2*9}=\frac{0}{18}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+21}{2*9}=\frac{42}{18}
=2+1/3
$