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

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

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

We move all terms to the left:

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses

p^2+p-234+2/3=0

We multiply all the terms by the denominator


p^2*3+p*3+2-234*3=0

We add all the numbers together, and all the variables

p^2*3+p*3-700=0

Wy multiply elements

3p^2+3p-700=0

a = 3; b = 3; c = -700;
Δ = b2-4ac
Δ = 32-4·3·(-700)
Δ = 8409
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{8409}}{2*3}=\frac{-3-\sqrt{8409}}{6}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{8409}}{2*3}=\frac{-3+\sqrt{8409}}{6}
$