3/5p+8-p=0

Solution for 3/5p+8-p=0 equation:

3/5p+8-p=0


Domain of the equation: 5p!=0

p!=0/5

p!=0

p∈R


We add all the numbers together, and all the variables

-1p+3/5p+8=0

We multiply all the terms by the denominator


-1p*5p+8*5p+3=0

Wy multiply elements

-5p^2+40p+3=0

a = -5; b = 40; c = +3;
Δ = b2-4ac
Δ = 402-4·(-5)·3
Δ = 1660
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:

$\sqrt{\Delta}=\sqrt{1660}=\sqrt{4*415}=\sqrt{4}*\sqrt{415}=2\sqrt{415}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-2\sqrt{415}}{2*-5}=\frac{-40-2\sqrt{415}}{-10}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+2\sqrt{415}}{2*-5}=\frac{-40+2\sqrt{415}}{-10}
$