6x(4x+8)=180

Solution for 6x(4x+8)=180 equation:

6x(4x+8)=180

We move all terms to the left:

6x(4x+8)-(180)=0

We multiply parentheses

24x^2+48x-180=0

a = 24; b = 48; c = -180;
Δ = b2-4ac
Δ = 482-4·24·(-180)
Δ = 19584
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:

$\sqrt{\Delta}=\sqrt{19584}=\sqrt{576*34}=\sqrt{576}*\sqrt{34}=24\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-24\sqrt{34}}{2*24}=\frac{-48-24\sqrt{34}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+24\sqrt{34}}{2*24}=\frac{-48+24\sqrt{34}}{48}
$