Y=x^2-12x+33

Solution for Y=x^2-12x+33 equation:

=Y^2-12Y+33

We move all terms to the left:

-(Y^2-12Y+33)=0

We get rid of parentheses

-Y^2+12Y-33=0

We add all the numbers together, and all the variables

-1Y^2+12Y-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:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

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