5p^2-9p+1=-3

Solution for 5p^2-9p+1=-3 equation:

5p^2-9p+1=-3

We move all terms to the left:

5p^2-9p+1-(-3)=0

We add all the numbers together, and all the variables

5p^2-9p+4=0

a = 5; b = -9; c = +4;
Δ = b2-4ac
Δ = -92-4·5·4
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-1}{2*5}=\frac{8}{10}
=4/5
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+1}{2*5}=\frac{10}{10}
=1
$