1/3p+2/9p=10

Solution for 1/3p+2/9p=10 equation:

1/3p+2/9p=10

We move all terms to the left:

1/3p+2/9p-(10)=0


Domain of the equation: 3p!=0

p!=0/3

p!=0

p∈R



Domain of the equation: 9p!=0

p!=0/9

p!=0

p∈R


We calculate fractions


9p/27p^2+6p/27p^2-10=0

We multiply all the terms by the denominator


9p+6p-10*27p^2=0

We add all the numbers together, and all the variables

15p-10*27p^2=0

Wy multiply elements

-270p^2+15p=0

a = -270; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·(-270)·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15}{2*-270}=\frac{-30}{-540}
=1/18
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*-270}=\frac{0}{-540}
=0
$