16-3p=3/2p+5

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

16-3p=3/2p+5

We move all terms to the left:

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


Domain of the equation: 2p+5)!=0

p∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-6p^2-10p+32p-3=0

We add all the numbers together, and all the variables

-6p^2+22p-3=0

a = -6; b = 22; c = -3;
Δ = b2-4ac
Δ = 222-4·(-6)·(-3)
Δ = 412
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:

$\sqrt{\Delta}=\sqrt{412}=\sqrt{4*103}=\sqrt{4}*\sqrt{103}=2\sqrt{103}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{103}}{2*-6}=\frac{-22-2\sqrt{103}}{-12}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{103}}{2*-6}=\frac{-22+2\sqrt{103}}{-12}
$