(359+5p^2)/(15+5p)=20

Solution for (359+5p^2)/(15+5p)=20 equation:

(359+5p^2)/(15+5p)=20

We move all terms to the left:

(359+5p^2)/(15+5p)-(20)=0


Domain of the equation: (15+5p)!=0

We move all terms containing p to the left, all other terms to the right

5p!=-15

p!=-15/5

p!=-3

p∈R


We add all the numbers together, and all the variables

(359+5p^2)/(5p+15)-20=0

We multiply all the terms by the denominator


(359+5p^2)-20*(5p+15)=0

We multiply parentheses

(359+5p^2)-100p-300=0

We get rid of parentheses

5p^2-100p+359-300=0

We add all the numbers together, and all the variables

5p^2-100p+59=0

a = 5; b = -100; c = +59;
Δ = b2-4ac
Δ = -1002-4·5·59
Δ = 8820
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:

$\sqrt{\Delta}=\sqrt{8820}=\sqrt{1764*5}=\sqrt{1764}*\sqrt{5}=42\sqrt{5}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-42\sqrt{5}}{2*5}=\frac{100-42\sqrt{5}}{10}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+42\sqrt{5}}{2*5}=\frac{100+42\sqrt{5}}{10}
$