p+1/3p-10=-2/3p+20

Solution for p+1/3p-10=-2/3p+20 equation:

p+1/3p-10=-2/3p+20

We move all terms to the left:

p+1/3p-10-(-2/3p+20)=0


Domain of the equation: 3p!=0

p!=0/3

p!=0

p∈R



Domain of the equation: 3p+20)!=0

p∈R


We get rid of parentheses

p+1/3p+2/3p-20-10=0

We multiply all the terms by the denominator


p*3p-20*3p-10*3p+1+2=0

We add all the numbers together, and all the variables

p*3p-20*3p-10*3p+3=0

Wy multiply elements

3p^2-60p-30p+3=0

We add all the numbers together, and all the variables

3p^2-90p+3=0

a = 3; b = -90; c = +3;
Δ = b2-4ac
Δ = -902-4·3·3
Δ = 8064
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:

$\sqrt{\Delta}=\sqrt{8064}=\sqrt{576*14}=\sqrt{576}*\sqrt{14}=24\sqrt{14}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-24\sqrt{14}}{2*3}=\frac{90-24\sqrt{14}}{6}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+24\sqrt{14}}{2*3}=\frac{90+24\sqrt{14}}{6}
$