p2+8p-22=0

Solution for p2+8p-22=0 equation:

p2+8p-22=0

We add all the numbers together, and all the variables

p^2+8p-22=0

a = 1; b = 8; c = -22;
Δ = b2-4ac
Δ = 82-4·1·(-22)
Δ = 152
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:

$\sqrt{\Delta}=\sqrt{152}=\sqrt{4*38}=\sqrt{4}*\sqrt{38}=2\sqrt{38}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{38}}{2*1}=\frac{-8-2\sqrt{38}}{2}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{38}}{2*1}=\frac{-8+2\sqrt{38}}{2}
$