p^2+5p=84=0

Solution for p^2+5p=84=0 equation:

p^2+5p=84=0

We move all terms to the left:

p^2+5p-(84)=0

a = 1; b = 5; c = -84;
Δ = b2-4ac
Δ = 52-4·1·(-84)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-19}{2*1}=\frac{-24}{2}
=-12
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+19}{2*1}=\frac{14}{2}
=7
$