533=4p^2+92

Solution for 533=4p^2+92 equation:

533=4p^2+92

We move all terms to the left:

533-(4p^2+92)=0

We get rid of parentheses

-4p^2-92+533=0

We add all the numbers together, and all the variables

-4p^2+441=0

a = -4; b = 0; c = +441;
Δ = b2-4ac
Δ = 02-4·(-4)·441
Δ = 7056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7056}=84$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-84}{2*-4}=\frac{-84}{-8}
=10+1/2
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+84}{2*-4}=\frac{84}{-8}
=-10+1/2
$