p^2+6p-42=8

Solution for p^2+6p-42=8 equation:

p^2+6p-42=8

We move all terms to the left:

p^2+6p-42-(8)=0

We add all the numbers together, and all the variables

p^2+6p-50=0

a = 1; b = 6; c = -50;
Δ = b2-4ac
Δ = 62-4·1·(-50)
Δ = 236
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:

$\sqrt{\Delta}=\sqrt{236}=\sqrt{4*59}=\sqrt{4}*\sqrt{59}=2\sqrt{59}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{59}}{2*1}=\frac{-6-2\sqrt{59}}{2}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{59}}{2*1}=\frac{-6+2\sqrt{59}}{2}
$