Y=x^2-6x-12

Solution for Y=x^2-6x-12 equation:

=Y^2-6Y-12

We move all terms to the left:

-(Y^2-6Y-12)=0

We get rid of parentheses

-Y^2+6Y+12=0

We add all the numbers together, and all the variables

-1Y^2+6Y+12=0

a = -1; b = 6; c = +12;
Δ = b2-4ac
Δ = 62-4·(-1)·12
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{21}}{2*-1}=\frac{-6-2\sqrt{21}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{21}}{2*-1}=\frac{-6+2\sqrt{21}}{-2}
$