Y=x^2-9x-18

Solution for Y=x^2-9x-18 equation:

=Y^2-9Y-18

We move all terms to the left:

-(Y^2-9Y-18)=0

We get rid of parentheses

-Y^2+9Y+18=0

We add all the numbers together, and all the variables

-1Y^2+9Y+18=0

a = -1; b = 9; c = +18;
Δ = b2-4ac
Δ = 92-4·(-1)·18
Δ = 153
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:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3\sqrt{17}}{2*-1}=\frac{-9-3\sqrt{17}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{17}}{2*-1}=\frac{-9+3\sqrt{17}}{-2}
$