3/8*p=3

Solution for 3/8*p=3 equation:

3/8*p=3

We move all terms to the left:

3/8*p-(3)=0


Domain of the equation: 8*p!=0

p!=0/1

p!=0

p∈R


We multiply all the terms by the denominator


-3*8*p+3=0

Wy multiply elements

-24p*p+3=0

Wy multiply elements

-24p^2+3=0

a = -24; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-24)·3
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{2}}{2*-24}=\frac{0-12\sqrt{2}}{-48}
=-\frac{12\sqrt{2}}{-48}
=-\frac{\sqrt{2}}{-4}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{2}}{2*-24}=\frac{0+12\sqrt{2}}{-48}
=\frac{12\sqrt{2}}{-48}
=\frac{\sqrt{2}}{-4}
$