(x+2)(3x+15)=42

Solution for (x+2)(3x+15)=42 equation:

(x+2)(3x+15)=42

We move all terms to the left:

(x+2)(3x+15)-(42)=0

We multiply parentheses ..

(+3x^2+15x+6x+30)-42=0

We get rid of parentheses

3x^2+15x+6x+30-42=0

We add all the numbers together, and all the variables

3x^2+21x-12=0

a = 3; b = 21; c = -12;
Δ = b2-4ac
Δ = 212-4·3·(-12)
Δ = 585
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:

$\sqrt{\Delta}=\sqrt{585}=\sqrt{9*65}=\sqrt{9}*\sqrt{65}=3\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-3\sqrt{65}}{2*3}=\frac{-21-3\sqrt{65}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+3\sqrt{65}}{2*3}=\frac{-21+3\sqrt{65}}{6}
$