5/7p+2/p=9

Solution for 5/7p+2/p=9 equation:

5/7p+2/p=9

We move all terms to the left:

5/7p+2/p-(9)=0


Domain of the equation: 7p!=0

p!=0/7

p!=0

p∈R



Domain of the equation: p!=0

p∈R


We calculate fractions


5p/7p^2+14p/7p^2-9=0

We multiply all the terms by the denominator


5p+14p-9*7p^2=0

We add all the numbers together, and all the variables

19p-9*7p^2=0

Wy multiply elements

-63p^2+19p=0

a = -63; b = 19; c = 0;
Δ = b2-4ac
Δ = 192-4·(-63)·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-19}{2*-63}=\frac{-38}{-126}
=19/63
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+19}{2*-63}=\frac{0}{-126}
=0
$