(x+2)(3x-12)=45

Solution for (x+2)(3x-12)=45 equation:

(x+2)(3x-12)=45

We move all terms to the left:

(x+2)(3x-12)-(45)=0

We multiply parentheses ..

(+3x^2-12x+6x-24)-45=0

We get rid of parentheses

3x^2-12x+6x-24-45=0

We add all the numbers together, and all the variables

3x^2-6x-69=0

a = 3; b = -6; c = -69;
Δ = b2-4ac
Δ = -62-4·3·(-69)
Δ = 864
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:

$\sqrt{\Delta}=\sqrt{864}=\sqrt{144*6}=\sqrt{144}*\sqrt{6}=12\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-12\sqrt{6}}{2*3}=\frac{6-12\sqrt{6}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+12\sqrt{6}}{2*3}=\frac{6+12\sqrt{6}}{6}
$