Y=x^2-22x+16

Solution for Y=x^2-22x+16 equation:

=Y^2-22Y+16

We move all terms to the left:

-(Y^2-22Y+16)=0

We get rid of parentheses

-Y^2+22Y-16=0

We add all the numbers together, and all the variables

-1Y^2+22Y-16=0

a = -1; b = 22; c = -16;
Δ = b2-4ac
Δ = 222-4·(-1)·(-16)
Δ = 420
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:

$\sqrt{\Delta}=\sqrt{420}=\sqrt{4*105}=\sqrt{4}*\sqrt{105}=2\sqrt{105}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{105}}{2*-1}=\frac{-22-2\sqrt{105}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{105}}{2*-1}=\frac{-22+2\sqrt{105}}{-2}
$