Y=5p^2-9p+4

Solution for Y=5p^2-9p+4 equation:

=5Y^2-9Y+4

We move all terms to the left:

-(5Y^2-9Y+4)=0

We get rid of parentheses

-5Y^2+9Y-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:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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