(3x+15)(x+2)=84

Solution for (3x+15)(x+2)=84 equation:

(3x+15)(x+2)=84

We move all terms to the left:

(3x+15)(x+2)-(84)=0

We multiply parentheses ..

(+3x^2+6x+15x+30)-84=0

We get rid of parentheses

3x^2+6x+15x+30-84=0

We add all the numbers together, and all the variables

3x^2+21x-54=0

a = 3; b = 21; c = -54;
Δ = b2-4ac
Δ = 212-4·3·(-54)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-33}{2*3}=\frac{-54}{6}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+33}{2*3}=\frac{12}{6}
=2
$