1/4p+3=p+8

Solution for 1/4p+3=p+8 equation:

1/4p+3=p+8

We move all terms to the left:

1/4p+3-(p+8)=0


Domain of the equation: 4p!=0

p!=0/4

p!=0

p∈R


We get rid of parentheses

1/4p-p-8+3=0

We multiply all the terms by the denominator


-p*4p-8*4p+3*4p+1=0

Wy multiply elements

-4p^2-32p+12p+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 = 416
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:

$\sqrt{\Delta}=\sqrt{416}=\sqrt{16*26}=\sqrt{16}*\sqrt{26}=4\sqrt{26}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{26}}{2*-4}=\frac{20-4\sqrt{26}}{-8}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{26}}{2*-4}=\frac{20+4\sqrt{26}}{-8}
$