p^2+14p-17=0

Solution for p^2+14p-17=0 equation:

p^2+14p-17=0

a = 1; b = 14; c = -17;
Δ = b2-4ac
Δ = 142-4·1·(-17)
Δ = 264
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{264}=\sqrt{4*66}=\sqrt{4}*\sqrt{66}=2\sqrt{66}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{66}}{2*1}=\frac{-14-2\sqrt{66}}{2}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{66}}{2*1}=\frac{-14+2\sqrt{66}}{2}
$