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

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

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

We move all terms to the left:

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


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

3x(2x-4)

We multiply parentheses

6x^2-12x

Back to the equation:

-(6x^2-12x)


We get rid of parentheses

-6x^2+9x+12x-12=0

We add all the numbers together, and all the variables

-6x^2+21x-12=0

a = -6; b = 21; c = -12;
Δ = b2-4ac
Δ = 212-4·(-6)·(-12)
Δ = 153
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-3\sqrt{17}}{2*-6}=\frac{-21-3\sqrt{17}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+3\sqrt{17}}{2*-6}=\frac{-21+3\sqrt{17}}{-12}
$