21=3x(x+2)

Solution for 21=3x(x+2) equation:

21=3x(x+2)

We move all terms to the left:

21-(3x(x+2))=0


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

3x(x+2)

We multiply parentheses

3x^2+6x

Back to the equation:

-(3x^2+6x)


We get rid of parentheses

-3x^2-6x+21=0

a = -3; b = -6; c = +21;
Δ = b2-4ac
Δ = -62-4·(-3)·21
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-12\sqrt{2}}{2*-3}=\frac{6-12\sqrt{2}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+12\sqrt{2}}{2*-3}=\frac{6+12\sqrt{2}}{-6}
$