x2-12x-133=280

Solution for x2-12x-133=280 equation:

x2-12x-133=280

We move all terms to the left:

x2-12x-133-(280)=0

We add all the numbers together, and all the variables

x^2-12x-413=0

a = 1; b = -12; c = -413;
Δ = b2-4ac
Δ = -122-4·1·(-413)
Δ = 1796
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:

$\sqrt{\Delta}=\sqrt{1796}=\sqrt{4*449}=\sqrt{4}*\sqrt{449}=2\sqrt{449}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{449}}{2*1}=\frac{12-2\sqrt{449}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{449}}{2*1}=\frac{12+2\sqrt{449}}{2}
$