2x(3x-12)+(4x+9)=x

Solution for 2x(3x-12)+(4x+9)=x equation:

2x(3x-12)+(4x+9)=x

We move all terms to the left:

2x(3x-12)+(4x+9)-(x)=0

We add all the numbers together, and all the variables

-1x+2x(3x-12)+(4x+9)=0

We multiply parentheses

6x^2-1x-24x+(4x+9)=0

We get rid of parentheses

6x^2-1x-24x+4x+9=0

We add all the numbers together, and all the variables

6x^2-21x+9=0

a = 6; b = -21; c = +9;
Δ = b2-4ac
Δ = -212-4·6·9
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-15}{2*6}=\frac{6}{12}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+15}{2*6}=\frac{36}{12}
=3
$