3p(1+5/3)=31/2

Solution for 3p(1+5/3)=31/2 equation:

3p(1+5/3)=31/2

We move all terms to the left:

3p(1+5/3)-(31/2)=0

We add all the numbers together, and all the variables

3p(5/3+1)-(+31/2)=0

We multiply parentheses

15p^2+3p-(+31/2)=0

We get rid of parentheses

15p^2+3p-31/2=0

We multiply all the terms by the denominator


15p^2*2+3p*2-31=0

Wy multiply elements

30p^2+6p-31=0

a = 30; b = 6; c = -31;
Δ = b2-4ac
Δ = 62-4·30·(-31)
Δ = 3756
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:

$\sqrt{\Delta}=\sqrt{3756}=\sqrt{4*939}=\sqrt{4}*\sqrt{939}=2\sqrt{939}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{939}}{2*30}=\frac{-6-2\sqrt{939}}{60}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{939}}{2*30}=\frac{-6+2\sqrt{939}}{60}
$