2/4p+6=2p+12

Solution for 2/4p+6=2p+12 equation:

2/4p+6=2p+12

We move all terms to the left:

2/4p+6-(2p+12)=0


Domain of the equation: 4p!=0

p!=0/4

p!=0

p∈R


We get rid of parentheses

2/4p-2p-12+6=0

We multiply all the terms by the denominator


-2p*4p-12*4p+6*4p+2=0

Wy multiply elements

-8p^2-48p+24p+2=0

We add all the numbers together, and all the variables

-8p^2-24p+2=0

a = -8; b = -24; c = +2;
Δ = b2-4ac
Δ = -242-4·(-8)·2
Δ = 640
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:

$\sqrt{\Delta}=\sqrt{640}=\sqrt{64*10}=\sqrt{64}*\sqrt{10}=8\sqrt{10}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-8\sqrt{10}}{2*-8}=\frac{24-8\sqrt{10}}{-16}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+8\sqrt{10}}{2*-8}=\frac{24+8\sqrt{10}}{-16}
$