12p-(3/p)=5

Solution for 12p-(3/p)=5 equation:

12p-(3/p)=5

We move all terms to the left:

12p-(3/p)-(5)=0


Domain of the equation: p)!=0

p!=0/1

p!=0

p∈R


We add all the numbers together, and all the variables

12p-(+3/p)-5=0

We get rid of parentheses

12p-3/p-5=0

We multiply all the terms by the denominator


12p*p-5*p-3=0

We add all the numbers together, and all the variables

-5p+12p*p-3=0

Wy multiply elements

12p^2-5p-3=0

a = 12; b = -5; c = -3;
Δ = b2-4ac
Δ = -52-4·12·(-3)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-13}{2*12}=\frac{-8}{24}
=-1/3
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+13}{2*12}=\frac{18}{24}
=3/4
$