y2+14y+33=0

Solution for y2+14y+33=0 equation:

y2+14y+33=0

We add all the numbers together, and all the variables

y^2+14y+33=0

a = 1; b = 14; c = +33;
Δ = b2-4ac
Δ = 142-4·1·33
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-8}{2*1}=\frac{-22}{2}
=-11
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+8}{2*1}=\frac{-6}{2}
=-3
$