1/2p+7=3/4p-9

Solution for 1/2p+7=3/4p-9 equation:

1/2p+7=3/4p-9

We move all terms to the left:

1/2p+7-(3/4p-9)=0


Domain of the equation: 2p!=0

p!=0/2

p!=0

p∈R



Domain of the equation: 4p-9)!=0

p∈R


We get rid of parentheses

1/2p-3/4p+9+7=0

We calculate fractions


4p/8p^2+(-6p)/8p^2+9+7=0

We add all the numbers together, and all the variables

4p/8p^2+(-6p)/8p^2+16=0

We multiply all the terms by the denominator


4p+(-6p)+16*8p^2=0

Wy multiply elements

128p^2+4p+(-6p)=0

We get rid of parentheses

128p^2+4p-6p=0

We add all the numbers together, and all the variables

128p^2-2p=0

a = 128; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·128·0
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*128}=\frac{0}{256}
=0
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*128}=\frac{4}{256}
=1/64
$