5/9p-2/7p+12=6

Solution for 5/9p-2/7p+12=6 equation:

5/9p-2/7p+12=6

We move all terms to the left:

5/9p-2/7p+12-(6)=0


Domain of the equation: 9p!=0

p!=0/9

p!=0

p∈R



Domain of the equation: 7p!=0

p!=0/7

p!=0

p∈R


We add all the numbers together, and all the variables

5/9p-2/7p+6=0

We calculate fractions


35p/63p^2+(-18p)/63p^2+6=0

We multiply all the terms by the denominator


35p+(-18p)+6*63p^2=0

Wy multiply elements

378p^2+35p+(-18p)=0

We get rid of parentheses

378p^2+35p-18p=0

We add all the numbers together, and all the variables

378p^2+17p=0

a = 378; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·378·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*378}=\frac{-34}{756}
=-17/378
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*378}=\frac{0}{756}
=0
$