16-3p=2/5p+5

Solution for 16-3p=2/5p+5 equation:

16-3p=2/5p+5

We move all terms to the left:

16-3p-(2/5p+5)=0


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

p∈R


We get rid of parentheses

-3p-2/5p-5+16=0

We multiply all the terms by the denominator


-3p*5p-5*5p+16*5p-2=0

Wy multiply elements

-15p^2-25p+80p-2=0

We add all the numbers together, and all the variables

-15p^2+55p-2=0

a = -15; b = 55; c = -2;
Δ = b2-4ac
Δ = 552-4·(-15)·(-2)
Δ = 2905
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(55)-\sqrt{2905}}{2*-15}=\frac{-55-\sqrt{2905}}{-30}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+\sqrt{2905}}{2*-15}=\frac{-55+\sqrt{2905}}{-30}
$