-7/9p+1/2p+2/9p=-1/8

Solution for -7/9p+1/2p+2/9p=-1/8 equation:

-7/9p+1/2p+2/9p=-1/8

We move all terms to the left:

-7/9p+1/2p+2/9p-(-1/8)=0


Domain of the equation: 9p!=0

p!=0/9

p!=0

p∈R



Domain of the equation: 2p!=0

p!=0/2

p!=0

p∈R


We get rid of parentheses

-7/9p+1/2p+2/9p+1/8=0

We calculate fractions


36p^2/1152p^2+(256p-7)/1152p^2+576p/1152p^2=0

We multiply all the terms by the denominator


36p^2+(256p-7)+576p=0

We add all the numbers together, and all the variables

36p^2+576p+(256p-7)=0

We get rid of parentheses

36p^2+576p+256p-7=0

We add all the numbers together, and all the variables

36p^2+832p-7=0

a = 36; b = 832; c = -7;
Δ = b2-4ac
Δ = 8322-4·36·(-7)
Δ = 693232
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:

$\sqrt{\Delta}=\sqrt{693232}=\sqrt{16*43327}=\sqrt{16}*\sqrt{43327}=4\sqrt{43327}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(832)-4\sqrt{43327}}{2*36}=\frac{-832-4\sqrt{43327}}{72}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(832)+4\sqrt{43327}}{2*36}=\frac{-832+4\sqrt{43327}}{72}
$