3/2p+9/4=1/12p-17

Solution for 3/2p+9/4=1/12p-17 equation:

3/2p+9/4=1/12p-17

We move all terms to the left:

3/2p+9/4-(1/12p-17)=0


Domain of the equation: 2p!=0

p!=0/2

p!=0

p∈R



Domain of the equation: 12p-17)!=0

p∈R


We get rid of parentheses

3/2p-1/12p+17+9/4=0

We calculate fractions


216p^2/384p^2+576p/384p^2+(-32p)/384p^2+17=0

We multiply all the terms by the denominator


216p^2+576p+(-32p)+17*384p^2=0

Wy multiply elements

216p^2+6528p^2+576p+(-32p)=0

We get rid of parentheses

216p^2+6528p^2+576p-32p=0

We add all the numbers together, and all the variables

6744p^2+544p=0

a = 6744; b = 544; c = 0;
Δ = b2-4ac
Δ = 5442-4·6744·0
Δ = 295936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{295936}=544$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(544)-544}{2*6744}=\frac{-1088}{13488}
=-68/843
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(544)+544}{2*6744}=\frac{0}{13488}
=0
$