Y=x^2-16x+58

Solution for Y=x^2-16x+58 equation:

=Y^2-16Y+58

We move all terms to the left:

-(Y^2-16Y+58)=0

We get rid of parentheses

-Y^2+16Y-58=0

We add all the numbers together, and all the variables

-1Y^2+16Y-58=0

a = -1; b = 16; c = -58;
Δ = b2-4ac
Δ = 162-4·(-1)·(-58)
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{6}}{2*-1}=\frac{-16-2\sqrt{6}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{6}}{2*-1}=\frac{-16+2\sqrt{6}}{-2}
$