341=p*p+15

Solution for 341=p*p+15 equation:

341=p*p+15

We move all terms to the left:

341-(p*p+15)=0

We get rid of parentheses

-p*p-15+341=0

We add all the numbers together, and all the variables

-p*p+326=0

Wy multiply elements

-1p^2+326=0

a = -1; b = 0; c = +326;
Δ = b2-4ac
Δ = 02-4·(-1)·326
Δ = 1304
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:

$\sqrt{\Delta}=\sqrt{1304}=\sqrt{4*326}=\sqrt{4}*\sqrt{326}=2\sqrt{326}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{326}}{2*-1}=\frac{0-2\sqrt{326}}{-2}
=-\frac{2\sqrt{326}}{-2}
=-\frac{\sqrt{326}}{-1}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{326}}{2*-1}=\frac{0+2\sqrt{326}}{-2}
=\frac{2\sqrt{326}}{-2}
=\frac{\sqrt{326}}{-1}
$