X(3x-18)=21

Solution for X(3x-18)=21 equation:

X(3X-18)=21

We move all terms to the left:

X(3X-18)-(21)=0

We multiply parentheses

3X^2-18X-21=0

a = 3; b = -18; c = -21;
Δ = b2-4ac
Δ = -182-4·3·(-21)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-24}{2*3}=\frac{-6}{6}
=-1
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+24}{2*3}=\frac{42}{6}
=7
$