x^2-6x+9=60

Solution for x^2-6x+9=60 equation:

x^2-6x+9=60

We move all terms to the left:

x^2-6x+9-(60)=0

We add all the numbers together, and all the variables

x^2-6x-51=0

a = 1; b = -6; c = -51;
Δ = b2-4ac
Δ = -62-4·1·(-51)
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-4\sqrt{15}}{2*1}=\frac{6-4\sqrt{15}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+4\sqrt{15}}{2*1}=\frac{6+4\sqrt{15}}{2}
$