1/8p-6=1/4p+9

Solution for 1/8p-6=1/4p+9 equation:

1/8p-6=1/4p+9

We move all terms to the left:

1/8p-6-(1/4p+9)=0


Domain of the equation: 8p!=0

p!=0/8

p!=0

p∈R



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

p∈R


We get rid of parentheses

1/8p-1/4p-9-6=0

We calculate fractions


4p/32p^2+(-8p)/32p^2-9-6=0

We add all the numbers together, and all the variables

4p/32p^2+(-8p)/32p^2-15=0

We multiply all the terms by the denominator


4p+(-8p)-15*32p^2=0

Wy multiply elements

-480p^2+4p+(-8p)=0

We get rid of parentheses

-480p^2+4p-8p=0

We add all the numbers together, and all the variables

-480p^2-4p=0

a = -480; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-480)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*-480}=\frac{0}{-960}
=0
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-480}=\frac{8}{-960}
=-1/120
$