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

We add all the numbers together, and all the variables

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

We multiply parentheses

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

We add all the numbers together, and all the variables

3p^2-234=0

a = 3; b = 0; c = -234;
Δ = b2-4ac
Δ = 02-4·3·(-234)
Δ = 2808
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:

$\sqrt{\Delta}=\sqrt{2808}=\sqrt{36*78}=\sqrt{36}*\sqrt{78}=6\sqrt{78}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{78}}{2*3}=\frac{0-6\sqrt{78}}{6}
=-\frac{6\sqrt{78}}{6}
=-\sqrt{78}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{78}}{2*3}=\frac{0+6\sqrt{78}}{6}
=\frac{6\sqrt{78}}{6}
=\sqrt{78}
$