3x(x-3)=6(x+3)

Solution for 3x(x-3)=6(x+3) equation:

3x(x-3)=6(x+3)

We move all terms to the left:

3x(x-3)-(6(x+3))=0

We multiply parentheses

3x^2-9x-(6(x+3))=0


We calculate terms in parentheses: -(6(x+3)), so:

6(x+3)

We multiply parentheses

6x+18

Back to the equation:

-(6x+18)


We get rid of parentheses

3x^2-9x-6x-18=0

We add all the numbers together, and all the variables

3x^2-15x-18=0

a = 3; b = -15; c = -18;
Δ = b2-4ac
Δ = -152-4·3·(-18)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-21}{2*3}=\frac{-6}{6}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+21}{2*3}=\frac{36}{6}
=6
$