x^2+16x+33=0

Solution for x^2+16x+33=0 equation:

x^2+16x+33=0

a = 1; b = 16; c = +33;
Δ = b2-4ac
Δ = 162-4·1·33
Δ = 124
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{31}}{2*1}=\frac{-16-2\sqrt{31}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{31}}{2*1}=\frac{-16+2\sqrt{31}}{2}
$