3/2p-5+9/4=7-5/4p

Solution for 3/2p-5+9/4=7-5/4p equation:

3/2p-5+9/4=7-5/4p

We move all terms to the left:

3/2p-5+9/4-(7-5/4p)=0


Domain of the equation: 2p!=0

p!=0/2

p!=0

p∈R



Domain of the equation: 4p)!=0

p!=0/1

p!=0

p∈R


We add all the numbers together, and all the variables

3/2p-(-5/4p+7)-5+9/4=0

We get rid of parentheses

3/2p+5/4p-7-5+9/4=0

We calculate fractions


192p/128p^2+10p/128p^2+18p/128p^2-7-5=0

We add all the numbers together, and all the variables

192p/128p^2+10p/128p^2+18p/128p^2-12=0

We multiply all the terms by the denominator


192p+10p+18p-12*128p^2=0

We add all the numbers together, and all the variables

220p-12*128p^2=0

Wy multiply elements

-1536p^2+220p=0

a = -1536; b = 220; c = 0;
Δ = b2-4ac
Δ = 2202-4·(-1536)·0
Δ = 48400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{48400}=220$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(220)-220}{2*-1536}=\frac{-440}{-3072}
=55/384
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(220)+220}{2*-1536}=\frac{0}{-3072}
=0
$