3x(x+48)=180

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

3x(x+48)=180

We move all terms to the left:

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

We multiply parentheses

3x^2+144x-180=0

a = 3; b = 144; c = -180;
Δ = b2-4ac
Δ = 1442-4·3·(-180)
Δ = 22896
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:

$\sqrt{\Delta}=\sqrt{22896}=\sqrt{144*159}=\sqrt{144}*\sqrt{159}=12\sqrt{159}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(144)-12\sqrt{159}}{2*3}=\frac{-144-12\sqrt{159}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(144)+12\sqrt{159}}{2*3}=\frac{-144+12\sqrt{159}}{6}
$