Y=x^2+16x+59

Solution for Y=x^2+16x+59 equation:

=Y^2+16Y+59

We move all terms to the left:

-(Y^2+16Y+59)=0

We get rid of parentheses

-Y^2-16Y-59=0

We add all the numbers together, and all the variables

-1Y^2-16Y-59=0

a = -1; b = -16; c = -59;
Δ = b2-4ac
Δ = -162-4·(-1)·(-59)
Δ = 20
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:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{5}}{2*-1}=\frac{16-2\sqrt{5}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{5}}{2*-1}=\frac{16+2\sqrt{5}}{-2}
$