X(3x+48)=180

Solution for X(3x+48)=180 equation:

X(3X+48)=180

We move all terms to the left:

X(3X+48)-(180)=0

We multiply parentheses

3X^2+48X-180=0

a = 3; b = 48; c = -180;
Δ = b2-4ac
Δ = 482-4·3·(-180)
Δ = 4464
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:

$\sqrt{\Delta}=\sqrt{4464}=\sqrt{144*31}=\sqrt{144}*\sqrt{31}=12\sqrt{31}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-12\sqrt{31}}{2*3}=\frac{-48-12\sqrt{31}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+12\sqrt{31}}{2*3}=\frac{-48+12\sqrt{31}}{6}
$