p-8-2/5p=16

Solution for p-8-2/5p=16 equation:

p-8-2/5p=16

We move all terms to the left:

p-8-2/5p-(16)=0


Domain of the equation: 5p!=0

p!=0/5

p!=0

p∈R


We add all the numbers together, and all the variables

p-2/5p-24=0

We multiply all the terms by the denominator


p*5p-24*5p-2=0

Wy multiply elements

5p^2-120p-2=0

a = 5; b = -120; c = -2;
Δ = b2-4ac
Δ = -1202-4·5·(-2)
Δ = 14440
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:

$\sqrt{\Delta}=\sqrt{14440}=\sqrt{1444*10}=\sqrt{1444}*\sqrt{10}=38\sqrt{10}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-38\sqrt{10}}{2*5}=\frac{120-38\sqrt{10}}{10}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+38\sqrt{10}}{2*5}=\frac{120+38\sqrt{10}}{10}
$