(7/2-p)*p=5/2

Solution for (7/2-p)*p=5/2 equation:

(7/2-p)*p=5/2

We move all terms to the left:

(7/2-p)*p-(5/2)=0


Domain of the equation: 2-p)*p!=0

We move all terms containing p to the left, all other terms to the right

-p)*p!=-2

p!=-2/1

p!=-2

p∈R


We add all the numbers together, and all the variables

(-1p+7/2)*p-(+5/2)=0

We multiply parentheses

-1p^2+7p^2-(+5/2)=0

We get rid of parentheses

-1p^2+7p^2-5/2=0

We multiply all the terms by the denominator


-1p^2*2+7p^2*2-5=0

Wy multiply elements

-2p^2+14p^2-5=0

We add all the numbers together, and all the variables

12p^2-5=0

a = 12; b = 0; c = -5;
Δ = b2-4ac
Δ = 02-4·12·(-5)
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{15}}{2*12}=\frac{0-4\sqrt{15}}{24}
=-\frac{4\sqrt{15}}{24}
=-\frac{\sqrt{15}}{6}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{15}}{2*12}=\frac{0+4\sqrt{15}}{24}
=\frac{4\sqrt{15}}{24}
=\frac{\sqrt{15}}{6}
$