Y=x2-18x+64

Solution for Y=x2-18x+64 equation:

=Y2-18Y+64

We move all terms to the left:

-(Y2-18Y+64)=0

We add all the numbers together, and all the variables

-(+Y^2-18Y+64)=0

We get rid of parentheses

-Y^2+18Y-64=0

We add all the numbers together, and all the variables

-1Y^2+18Y-64=0

a = -1; b = 18; c = -64;
Δ = b2-4ac
Δ = 182-4·(-1)·(-64)
Δ = 68
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:

$\sqrt{\Delta}=\sqrt{68}=\sqrt{4*17}=\sqrt{4}*\sqrt{17}=2\sqrt{17}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{17}}{2*-1}=\frac{-18-2\sqrt{17}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{17}}{2*-1}=\frac{-18+2\sqrt{17}}{-2}
$