Y=x^2-6x-81

Solution for Y=x^2-6x-81 equation:

=Y^2-6Y-81

We move all terms to the left:

-(Y^2-6Y-81)=0

We get rid of parentheses

-Y^2+6Y+81=0

We add all the numbers together, and all the variables

-1Y^2+6Y+81=0

a = -1; b = 6; c = +81;
Δ = b2-4ac
Δ = 62-4·(-1)·81
Δ = 360
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:

$\sqrt{\Delta}=\sqrt{360}=\sqrt{36*10}=\sqrt{36}*\sqrt{10}=6\sqrt{10}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{10}}{2*-1}=\frac{-6-6\sqrt{10}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{10}}{2*-1}=\frac{-6+6\sqrt{10}}{-2}
$