3/2p=p+17

Solution for 3/2p=p+17 equation:

3/2p=p+17

We move all terms to the left:

3/2p-(p+17)=0


Domain of the equation: 2p!=0

p!=0/2

p!=0

p∈R


We get rid of parentheses

3/2p-p-17=0

We multiply all the terms by the denominator


-p*2p-17*2p+3=0

Wy multiply elements

-2p^2-34p+3=0

a = -2; b = -34; c = +3;
Δ = b2-4ac
Δ = -342-4·(-2)·3
Δ = 1180
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:

$\sqrt{\Delta}=\sqrt{1180}=\sqrt{4*295}=\sqrt{4}*\sqrt{295}=2\sqrt{295}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2\sqrt{295}}{2*-2}=\frac{34-2\sqrt{295}}{-4}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2\sqrt{295}}{2*-2}=\frac{34+2\sqrt{295}}{-4}
$