Y=x^2-21x-27

Solution for Y=x^2-21x-27 equation:

=Y^2-21Y-27

We move all terms to the left:

-(Y^2-21Y-27)=0

We get rid of parentheses

-Y^2+21Y+27=0

We add all the numbers together, and all the variables

-1Y^2+21Y+27=0

a = -1; b = 21; c = +27;
Δ = b2-4ac
Δ = 212-4·(-1)·27
Δ = 549
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:

$\sqrt{\Delta}=\sqrt{549}=\sqrt{9*61}=\sqrt{9}*\sqrt{61}=3\sqrt{61}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-3\sqrt{61}}{2*-1}=\frac{-21-3\sqrt{61}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+3\sqrt{61}}{2*-1}=\frac{-21+3\sqrt{61}}{-2}
$