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

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

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

We move all terms to the left:

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

We multiply parentheses

9x^2-27x-(-3(2x+4))=0


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

-3(2x+4)

We multiply parentheses

-6x-12

Back to the equation:

-(-6x-12)


We get rid of parentheses

9x^2-27x+6x+12=0

We add all the numbers together, and all the variables

9x^2-21x+12=0

a = 9; b = -21; c = +12;
Δ = b2-4ac
Δ = -212-4·9·12
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-3}{2*9}=\frac{18}{18}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+3}{2*9}=\frac{24}{18}
=1+1/3
$