1/2p+15=-1/4p+18

Solution for 1/2p+15=-1/4p+18 equation:

1/2p+15=-1/4p+18

We move all terms to the left:

1/2p+15-(-1/4p+18)=0


Domain of the equation: 2p!=0

p!=0/2

p!=0

p∈R



Domain of the equation: 4p+18)!=0

p∈R


We get rid of parentheses

1/2p+1/4p-18+15=0

We calculate fractions


4p/8p^2+2p/8p^2-18+15=0

We add all the numbers together, and all the variables

4p/8p^2+2p/8p^2-3=0

We multiply all the terms by the denominator


4p+2p-3*8p^2=0

We add all the numbers together, and all the variables

6p-3*8p^2=0

Wy multiply elements

-24p^2+6p=0

a = -24; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-24)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*-24}=\frac{-12}{-48}
=1/4
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-24}=\frac{0}{-48}
=0
$