x^2-16x-6=180

Solution for x^2-16x-6=180 equation:

x^2-16x-6=180

We move all terms to the left:

x^2-16x-6-(180)=0

We add all the numbers together, and all the variables

x^2-16x-186=0

a = 1; b = -16; c = -186;
Δ = b2-4ac
Δ = -162-4·1·(-186)
Δ = 1000
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:

$\sqrt{\Delta}=\sqrt{1000}=\sqrt{100*10}=\sqrt{100}*\sqrt{10}=10\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-10\sqrt{10}}{2*1}=\frac{16-10\sqrt{10}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+10\sqrt{10}}{2*1}=\frac{16+10\sqrt{10}}{2}
$