5p/7p+2/p=9

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

5p/7p+2/p=9

We move all terms to the left:

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

We multiply all the terms by the denominator


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

Wy multiply elements

5p^2-63p^2+14p=0

We add all the numbers together, and all the variables

-58p^2+14p=0

a = -58; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·(-58)·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14}{2*-58}=\frac{-28}{-116}
=7/29
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*-58}=\frac{0}{-116}
=0
$