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

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

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

We move all terms to the left:

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


Domain of the equation: 4p!=0

p!=0/4

p!=0

p∈R



Domain of the equation: 2p-3)!=0

p∈R


We get rid of parentheses

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

We calculate fractions


6p/8p^2+(-4p)/8p^2+3+9=0

We add all the numbers together, and all the variables

6p/8p^2+(-4p)/8p^2+12=0

We multiply all the terms by the denominator


6p+(-4p)+12*8p^2=0

Wy multiply elements

96p^2+6p+(-4p)=0

We get rid of parentheses

96p^2+6p-4p=0

We add all the numbers together, and all the variables

96p^2+2p=0

a = 96; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·96·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*96}=\frac{-4}{192}
=-1/48
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*96}=\frac{0}{192}
=0
$