Y=x2-12x-5

Solution for Y=x2-12x-5 equation:

=Y2-12Y-5

We move all terms to the left:

-(Y2-12Y-5)=0

We add all the numbers together, and all the variables

-(+Y^2-12Y-5)=0

We get rid of parentheses

-Y^2+12Y+5=0

We add all the numbers together, and all the variables

-1Y^2+12Y+5=0

a = -1; b = 12; c = +5;
Δ = b2-4ac
Δ = 122-4·(-1)·5
Δ = 164
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:

$\sqrt{\Delta}=\sqrt{164}=\sqrt{4*41}=\sqrt{4}*\sqrt{41}=2\sqrt{41}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{41}}{2*-1}=\frac{-12-2\sqrt{41}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{41}}{2*-1}=\frac{-12+2\sqrt{41}}{-2}
$