2+(12/p)=4p

Solution for 2+(12/p)=4p equation:

2+(12/p)=4p

We move all terms to the left:

2+(12/p)-(4p)=0


Domain of the equation: p)!=0

p!=0/1

p!=0

p∈R


We add all the numbers together, and all the variables

(+12/p)-4p+2=0

We add all the numbers together, and all the variables

-4p+(+12/p)+2=0

We get rid of parentheses

-4p+12/p+2=0

We multiply all the terms by the denominator


-4p*p+2*p+12=0

We add all the numbers together, and all the variables

2p-4p*p+12=0

Wy multiply elements

-4p^2+2p+12=0

a = -4; b = 2; c = +12;
Δ = b2-4ac
Δ = 22-4·(-4)·12
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-14}{2*-4}=\frac{-16}{-8}
=+2
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+14}{2*-4}=\frac{12}{-8}
=-1+1/2
$