y2+20y+51=0

Solution for y2+20y+51=0 equation:

y2+20y+51=0

We add all the numbers together, and all the variables

y^2+20y+51=0

a = 1; b = 20; c = +51;
Δ = b2-4ac
Δ = 202-4·1·51
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-14}{2*1}=\frac{-34}{2}
=-17
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+14}{2*1}=\frac{-6}{2}
=-3
$