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

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

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

We move all terms to the left:

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


Domain of the equation: 2p!=0

p!=0/2

p!=0

p∈R



Domain of the equation: 4p!=0

p!=0/4

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

We get rid of parentheses

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

We calculate fractions


12p/8p^2+(10p+9)/8p^2-7-5=0

We add all the numbers together, and all the variables

12p/8p^2+(10p+9)/8p^2-12=0

We multiply all the terms by the denominator


12p+(10p+9)-12*8p^2=0

Wy multiply elements

-96p^2+12p+(10p+9)=0

We get rid of parentheses

-96p^2+12p+10p+9=0

We add all the numbers together, and all the variables

-96p^2+22p+9=0

a = -96; b = 22; c = +9;
Δ = b2-4ac
Δ = 222-4·(-96)·9
Δ = 3940
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:

$\sqrt{\Delta}=\sqrt{3940}=\sqrt{4*985}=\sqrt{4}*\sqrt{985}=2\sqrt{985}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{985}}{2*-96}=\frac{-22-2\sqrt{985}}{-192}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{985}}{2*-96}=\frac{-22+2\sqrt{985}}{-192}
$