-5p+3=p2

Solution for -5p+3=p2 equation:

-5p+3=p2

We move all terms to the left:

-5p+3-(p2)=0

We add all the numbers together, and all the variables

-1p^2-5p+3=0

a = -1; b = -5; c = +3;
Δ = b2-4ac
Δ = -52-4·(-1)·3
Δ = 37
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{-(-5)-\sqrt{37}}{2*-1}=\frac{5-\sqrt{37}}{-2}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{37}}{2*-1}=\frac{5+\sqrt{37}}{-2}
$