X2-12x+33=0

Solution for X2-12x+33=0 equation:

X2-12X+33=0

We add all the numbers together, and all the variables

X^2-12X+33=0

a = 1; b = -12; c = +33;
Δ = b2-4ac
Δ = -122-4·1·33
Δ = 12
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:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{3}}{2*1}=\frac{12-2\sqrt{3}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{3}}{2*1}=\frac{12+2\sqrt{3}}{2}
$