p+(2/3)p+(1/2)p=234

Solution for p+(2/3)p+(1/2)p=234 equation:

p+(2/3)p+(1/2)p=234

We move all terms to the left:

p+(2/3)p+(1/2)p-(234)=0


Domain of the equation: 3)p!=0

p!=0/1

p!=0

p∈R



Domain of the equation: 2)p!=0

p!=0/1

p!=0

p∈R


We add all the numbers together, and all the variables

p+(+2/3)p+(+1/2)p-234=0

We multiply parentheses

2p^2+p^2+p-234=0

We add all the numbers together, and all the variables

3p^2+p-234=0

a = 3; b = 1; c = -234;
Δ = b2-4ac
Δ = 12-4·3·(-234)
Δ = 2809
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2809}=53$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-53}{2*3}=\frac{-54}{6}
=-9
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+53}{2*3}=\frac{52}{6}
=8+2/3
$