Y=-4x^2+5x+1

Solution for Y=-4x^2+5x+1 equation:

=-4Y^2+5Y+1

We move all terms to the left:

-(-4Y^2+5Y+1)=0

We get rid of parentheses

4Y^2-5Y-1=0

a = 4; b = -5; c = -1;
Δ = b2-4ac
Δ = -52-4·4·(-1)
Δ = 41
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{41}}{2*4}=\frac{5-\sqrt{41}}{8}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{41}}{2*4}=\frac{5+\sqrt{41}}{8}
$