y2+14=-9y

Solution for y2+14=-9y equation:

y2+14=-9y

We move all terms to the left:

y2+14-(-9y)=0

We add all the numbers together, and all the variables

y^2-(-9y)+14=0

We get rid of parentheses

y^2+9y+14=0

a = 1; b = 9; c = +14;
Δ = b2-4ac
Δ = 92-4·1·14
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-5}{2*1}=\frac{-14}{2}
=-7
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+5}{2*1}=\frac{-4}{2}
=-2
$