(3x+18)(5x+2)=180

Solution for (3x+18)(5x+2)=180 equation:

(3x+18)(5x+2)=180

We move all terms to the left:

(3x+18)(5x+2)-(180)=0

We multiply parentheses ..

(+15x^2+6x+90x+36)-180=0

We get rid of parentheses

15x^2+6x+90x+36-180=0

We add all the numbers together, and all the variables

15x^2+96x-144=0

a = 15; b = 96; c = -144;
Δ = b2-4ac
Δ = 962-4·15·(-144)
Δ = 17856
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:

$\sqrt{\Delta}=\sqrt{17856}=\sqrt{576*31}=\sqrt{576}*\sqrt{31}=24\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(96)-24\sqrt{31}}{2*15}=\frac{-96-24\sqrt{31}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(96)+24\sqrt{31}}{2*15}=\frac{-96+24\sqrt{31}}{30}
$