2/3p=10-p

Solution for 2/3p=10-p equation:

2/3p=10-p

We move all terms to the left:

2/3p-(10-p)=0


Domain of the equation: 3p!=0

p!=0/3

p!=0

p∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

2/3p+1p-10=0

We multiply all the terms by the denominator


1p*3p-10*3p+2=0

Wy multiply elements

3p^2-30p+2=0

a = 3; b = -30; c = +2;
Δ = b2-4ac
Δ = -302-4·3·2
Δ = 876
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:

$\sqrt{\Delta}=\sqrt{876}=\sqrt{4*219}=\sqrt{4}*\sqrt{219}=2\sqrt{219}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{219}}{2*3}=\frac{30-2\sqrt{219}}{6}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{219}}{2*3}=\frac{30+2\sqrt{219}}{6}
$