2/3p-5=21+p

Solution for 2/3p-5=21+p equation:

2/3p-5=21+p

We move all terms to the left:

2/3p-5-(21+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-(p+21)-5=0

We get rid of parentheses

2/3p-p-21-5=0

We multiply all the terms by the denominator


-p*3p-21*3p-5*3p+2=0

Wy multiply elements

-3p^2-63p-15p+2=0

We add all the numbers together, and all the variables

-3p^2-78p+2=0

a = -3; b = -78; c = +2;
Δ = b2-4ac
Δ = -782-4·(-3)·2
Δ = 6108
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:

$\sqrt{\Delta}=\sqrt{6108}=\sqrt{4*1527}=\sqrt{4}*\sqrt{1527}=2\sqrt{1527}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-78)-2\sqrt{1527}}{2*-3}=\frac{78-2\sqrt{1527}}{-6}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-78)+2\sqrt{1527}}{2*-3}=\frac{78+2\sqrt{1527}}{-6}
$