6x(x-16)=180

Solution for 6x(x-16)=180 equation:

6x(x-16)=180

We move all terms to the left:

6x(x-16)-(180)=0

We multiply parentheses

6x^2-96x-180=0

a = 6; b = -96; c = -180;
Δ = b2-4ac
Δ = -962-4·6·(-180)
Δ = 13536
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:

$\sqrt{\Delta}=\sqrt{13536}=\sqrt{144*94}=\sqrt{144}*\sqrt{94}=12\sqrt{94}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-12\sqrt{94}}{2*6}=\frac{96-12\sqrt{94}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+12\sqrt{94}}{2*6}=\frac{96+12\sqrt{94}}{12}
$