12x-4x(6x-9)=9x(4-2x)+3x

Solution for 12x-4x(6x-9)=9x(4-2x)+3x equation:

12x-4x(6x-9)=9x(4-2x)+3x

We move all terms to the left:

12x-4x(6x-9)-(9x(4-2x)+3x)=0

We add all the numbers together, and all the variables

12x-4x(6x-9)-(9x(-2x+4)+3x)=0

We multiply parentheses

-24x^2+12x+36x-(9x(-2x+4)+3x)=0


We calculate terms in parentheses: -(9x(-2x+4)+3x), so:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

-18x^2+3x+36x

We add all the numbers together, and all the variables

-18x^2+39x

Back to the equation:

-(-18x^2+39x)


We add all the numbers together, and all the variables

-24x^2-(-18x^2+39x)+48x=0

We get rid of parentheses

-24x^2+18x^2-39x+48x=0

We add all the numbers together, and all the variables

-6x^2+9x=0

a = -6; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-6)·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*-6}=\frac{-18}{-12}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-6}=\frac{0}{-12}
=0
$