(3p)2+(p)2=(8)2

Solution for (3p)2+(p)2=(8)2 equation:

(3p)2+(p)2=(8)2

We move all terms to the left:

(3p)2+(p)2-((8)2)=0

determiningTheFunctionDomain
3p2+p2-82=0

We add all the numbers together, and all the variables

4p^2-82=0

a = 4; b = 0; c = -82;
Δ = b2-4ac
Δ = 02-4·4·(-82)
Δ = 1312
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:

$\sqrt{\Delta}=\sqrt{1312}=\sqrt{16*82}=\sqrt{16}*\sqrt{82}=4\sqrt{82}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{82}}{2*4}=\frac{0-4\sqrt{82}}{8}
=-\frac{4\sqrt{82}}{8}
=-\frac{\sqrt{82}}{2}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{82}}{2*4}=\frac{0+4\sqrt{82}}{8}
=\frac{4\sqrt{82}}{8}
=\frac{\sqrt{82}}{2}
$