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+42p-3=0

a = -6; b = 42; c = -3;
Δ = b2-4ac
Δ = 422-4·(-6)·(-3)
Δ = 1692
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:

$\sqrt{\Delta}=\sqrt{1692}=\sqrt{36*47}=\sqrt{36}*\sqrt{47}=6\sqrt{47}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-6\sqrt{47}}{2*-6}=\frac{-42-6\sqrt{47}}{-12}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+6\sqrt{47}}{2*-6}=\frac{-42+6\sqrt{47}}{-12}
$