3x(3x+12)=x

Solution for 3x(3x+12)=x equation:

3x(3x+12)=x

We move all terms to the left:

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

We add all the numbers together, and all the variables

-1x+3x(3x+12)=0

We multiply parentheses

9x^2-1x+36x=0

We add all the numbers together, and all the variables

9x^2+35x=0

a = 9; b = 35; c = 0;
Δ = b2-4ac
Δ = 352-4·9·0
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-35}{2*9}=\frac{-70}{18}
=-3+8/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+35}{2*9}=\frac{0}{18}
=0
$