(x+2)(3x+15)=105

Solution for (x+2)(3x+15)=105 equation:

(x+2)(3x+15)=105

We move all terms to the left:

(x+2)(3x+15)-(105)=0

We multiply parentheses ..

(+3x^2+15x+6x+30)-105=0

We get rid of parentheses

3x^2+15x+6x+30-105=0

We add all the numbers together, and all the variables

3x^2+21x-75=0

a = 3; b = 21; c = -75;
Δ = b2-4ac
Δ = 212-4·3·(-75)
Δ = 1341
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:

$\sqrt{\Delta}=\sqrt{1341}=\sqrt{9*149}=\sqrt{9}*\sqrt{149}=3\sqrt{149}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-3\sqrt{149}}{2*3}=\frac{-21-3\sqrt{149}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+3\sqrt{149}}{2*3}=\frac{-21+3\sqrt{149}}{6}
$