3(x-3)=x(4x-12)

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

3(x-3)=x(4x-12)

We move all terms to the left:

3(x-3)-(x(4x-12))=0

We multiply parentheses

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


We calculate terms in parentheses: -(x(4x-12)), so:

x(4x-12)

We multiply parentheses

4x^2-12x

Back to the equation:

-(4x^2-12x)


We get rid of parentheses

-4x^2+3x+12x-9=0

We add all the numbers together, and all the variables

-4x^2+15x-9=0

a = -4; b = 15; c = -9;
Δ = b2-4ac
Δ = 152-4·(-4)·(-9)
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{-(15)-9}{2*-4}=\frac{-24}{-8}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+9}{2*-4}=\frac{-6}{-8}
=3/4
$