p-1/4p=750,000

Solution for p-1/4p=750,000 equation:

p-1/4p=750.000

We move all terms to the left:

p-1/4p-(750.000)=0


Domain of the equation: 4p!=0

p!=0/4

p!=0

p∈R


We add all the numbers together, and all the variables

p-1/4p-750=0

We multiply all the terms by the denominator


p*4p-750*4p-1=0

Wy multiply elements

4p^2-3000p-1=0

a = 4; b = -3000; c = -1;
Δ = b2-4ac
Δ = -30002-4·4·(-1)
Δ = 9000016
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:

$\sqrt{\Delta}=\sqrt{9000016}=\sqrt{16*562501}=\sqrt{16}*\sqrt{562501}=4\sqrt{562501}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3000)-4\sqrt{562501}}{2*4}=\frac{3000-4\sqrt{562501}}{8}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3000)+4\sqrt{562501}}{2*4}=\frac{3000+4\sqrt{562501}}{8}
$