x^2-6x+1=180

Solution for x^2-6x+1=180 equation:

x^2-6x+1=180

We move all terms to the left:

x^2-6x+1-(180)=0

We add all the numbers together, and all the variables

x^2-6x-179=0

a = 1; b = -6; c = -179;
Δ = b2-4ac
Δ = -62-4·1·(-179)
Δ = 752
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:

$\sqrt{\Delta}=\sqrt{752}=\sqrt{16*47}=\sqrt{16}*\sqrt{47}=4\sqrt{47}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-4\sqrt{47}}{2*1}=\frac{6-4\sqrt{47}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+4\sqrt{47}}{2*1}=\frac{6+4\sqrt{47}}{2}
$