1/4p+7=2-p

Solution for 1/4p+7=2-p equation:

1/4p+7=2-p

We move all terms to the left:

1/4p+7-(2-p)=0


Domain of the equation: 4p!=0

p!=0/4

p!=0

p∈R


We add all the numbers together, and all the variables

1/4p-(-1p+2)+7=0

We get rid of parentheses

1/4p+1p-2+7=0

We multiply all the terms by the denominator


1p*4p-2*4p+7*4p+1=0

Wy multiply elements

4p^2-8p+28p+1=0

We add all the numbers together, and all the variables

4p^2+20p+1=0

a = 4; b = 20; c = +1;
Δ = b2-4ac
Δ = 202-4·4·1
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-8\sqrt{6}}{2*4}=\frac{-20-8\sqrt{6}}{8}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+8\sqrt{6}}{2*4}=\frac{-20+8\sqrt{6}}{8}
$