x(3x-16)=180

Solution for x(3x-16)=180 equation:

x(3x-16)=180

We move all terms to the left:

x(3x-16)-(180)=0

We multiply parentheses

3x^2-16x-180=0

a = 3; b = -16; c = -180;
Δ = b2-4ac
Δ = -162-4·3·(-180)
Δ = 2416
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:

$\sqrt{\Delta}=\sqrt{2416}=\sqrt{16*151}=\sqrt{16}*\sqrt{151}=4\sqrt{151}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{151}}{2*3}=\frac{16-4\sqrt{151}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{151}}{2*3}=\frac{16+4\sqrt{151}}{6}
$