10=-2p-2/3p

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

10=-2p-2/3p

We move all terms to the left:

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


Domain of the equation: 3p)!=0

p!=0/1

p!=0

p∈R


We get rid of parentheses

2p+2/3p+10=0

We multiply all the terms by the denominator


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

Wy multiply elements

6p^2+30p+2=0

a = 6; b = 30; c = +2;
Δ = b2-4ac
Δ = 302-4·6·2
Δ = 852
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:

$\sqrt{\Delta}=\sqrt{852}=\sqrt{4*213}=\sqrt{4}*\sqrt{213}=2\sqrt{213}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{213}}{2*6}=\frac{-30-2\sqrt{213}}{12}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{213}}{2*6}=\frac{-30+2\sqrt{213}}{12}
$