k^2+14k+15=0

Solution for k^2+14k+15=0 equation:

k^2+14k+15=0

a = 1; b = 14; c = +15;
Δ = b2-4ac
Δ = 142-4·1·15
Δ = 136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{34}}{2*1}=\frac{-14-2\sqrt{34}}{2}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{34}}{2*1}=\frac{-14+2\sqrt{34}}{2}
$