p^2+50p=75000

Solution for p^2+50p=75000 equation:

p^2+50p=75000

We move all terms to the left:

p^2+50p-(75000)=0

a = 1; b = 50; c = -75000;
Δ = b2-4ac
Δ = 502-4·1·(-75000)
Δ = 302500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{302500}=550$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-550}{2*1}=\frac{-600}{2}
=-300
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+550}{2*1}=\frac{500}{2}
=250
$