0.30=800p-10000/800p

Solution for 0.30=800p-10000/800p equation:

0.30=800p-10000/800p

We move all terms to the left:

0.30-(800p-10000/800p)=0


Domain of the equation: 800p)!=0

p!=0/1

p!=0

p∈R


We add all the numbers together, and all the variables

-(+800p-10000/800p)+0.30=0

We add all the numbers together, and all the variables

-(+800p-10000/800p)+0.3=0

We get rid of parentheses

-800p+10000/800p+0.3=0

We multiply all the terms by the denominator


-800p*800p+(0.3)*800p+10000=0

We multiply parentheses

-800p*800p+240p+10000=0

Wy multiply elements

-640000p^2+240p+10000=0

a = -640000; b = 240; c = +10000;
Δ = b2-4ac
Δ = 2402-4·(-640000)·10000
Δ = 25600057600
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:

$\sqrt{\Delta}=\sqrt{25600057600}=\sqrt{6400*4000009}=\sqrt{6400}*\sqrt{4000009}=80\sqrt{4000009}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(240)-80\sqrt{4000009}}{2*-640000}=\frac{-240-80\sqrt{4000009}}{-1280000}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(240)+80\sqrt{4000009}}{2*-640000}=\frac{-240+80\sqrt{4000009}}{-1280000}
$