200p-5000/200p=0.3

Solution for 200p-5000/200p=0.3 equation:

200p-5000/200p=0.3

We move all terms to the left:

200p-5000/200p-(0.3)=0


Domain of the equation: 200p!=0

p!=0/200

p!=0

p∈R


We add all the numbers together, and all the variables

200p-5000/200p-0.3=0

We multiply all the terms by the denominator


200p*200p-(0.3)*200p-5000=0

We multiply parentheses

200p*200p-60p-5000=0

Wy multiply elements

40000p^2-60p-5000=0

a = 40000; b = -60; c = -5000;
Δ = b2-4ac
Δ = -602-4·40000·(-5000)
Δ = 800003600
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:

$\sqrt{\Delta}=\sqrt{800003600}=\sqrt{48400*16529}=\sqrt{48400}*\sqrt{16529}=220\sqrt{16529}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-220\sqrt{16529}}{2*40000}=\frac{60-220\sqrt{16529}}{80000}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+220\sqrt{16529}}{2*40000}=\frac{60+220\sqrt{16529}}{80000}
$