(3x-6)(x+48)=180

Solution for (3x-6)(x+48)=180 equation:

(3x-6)(x+48)=180

We move all terms to the left:

(3x-6)(x+48)-(180)=0

We multiply parentheses ..

(+3x^2+144x-6x-288)-180=0

We get rid of parentheses

3x^2+144x-6x-288-180=0

We add all the numbers together, and all the variables

3x^2+138x-468=0

a = 3; b = 138; c = -468;
Δ = b2-4ac
Δ = 1382-4·3·(-468)
Δ = 24660
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:

$\sqrt{\Delta}=\sqrt{24660}=\sqrt{36*685}=\sqrt{36}*\sqrt{685}=6\sqrt{685}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(138)-6\sqrt{685}}{2*3}=\frac{-138-6\sqrt{685}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(138)+6\sqrt{685}}{2*3}=\frac{-138+6\sqrt{685}}{6}
$