X(3x+6)=45

Solution for X(3x+6)=45 equation:

X(3X+6)=45

We move all terms to the left:

X(3X+6)-(45)=0

We multiply parentheses

3X^2+6X-45=0

a = 3; b = 6; c = -45;
Δ = b2-4ac
Δ = 62-4·3·(-45)
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{-(6)-24}{2*3}=\frac{-30}{6}
=-5
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+24}{2*3}=\frac{18}{6}
=3
$