10-p=2/3p

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

10-p=2/3p

We move all terms to the left:

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


Domain of the equation: 3p)!=0

p!=0/1

p!=0

p∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

-1p-2/3p+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}
$