y2+14y=-39

Solution for y2+14y=-39 equation:

y2+14y=-39

We move all terms to the left:

y2+14y-(-39)=0

We add all the numbers together, and all the variables

y^2+14y+39=0

a = 1; b = 14; c = +39;
Δ = b2-4ac
Δ = 142-4·1·39
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{10}}{2*1}=\frac{-14-2\sqrt{10}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{10}}{2*1}=\frac{-14+2\sqrt{10}}{2}
$