150000=1/3*p

Solution for 150000=1/3*p equation:

150000=1/3*p

We move all terms to the left:

150000-(1/3*p)=0


Domain of the equation: 3*p)!=0

p!=0/1

p!=0

p∈R


We add all the numbers together, and all the variables

-(+1/3*p)+150000=0

We get rid of parentheses

-1/3*p+150000=0

We multiply all the terms by the denominator


150000*3*p-1=0

Wy multiply elements

450000p*p-1=0

Wy multiply elements

450000p^2-1=0

a = 450000; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·450000·(-1)
Δ = 1800000
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:

$\sqrt{\Delta}=\sqrt{1800000}=\sqrt{360000*5}=\sqrt{360000}*\sqrt{5}=600\sqrt{5}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-600\sqrt{5}}{2*450000}=\frac{0-600\sqrt{5}}{900000}
=-\frac{600\sqrt{5}}{900000}
=-\frac{\sqrt{5}}{1500}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+600\sqrt{5}}{2*450000}=\frac{0+600\sqrt{5}}{900000}
=\frac{600\sqrt{5}}{900000}
=\frac{\sqrt{5}}{1500}
$