Y=-5x^2+25x+3

Solution for Y=-5x^2+25x+3 equation:

=-5Y^2+25Y+3

We move all terms to the left:

-(-5Y^2+25Y+3)=0

We get rid of parentheses

5Y^2-25Y-3=0

a = 5; b = -25; c = -3;
Δ = b2-4ac
Δ = -252-4·5·(-3)
Δ = 685
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{-(-25)-\sqrt{685}}{2*5}=\frac{25-\sqrt{685}}{10}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+\sqrt{685}}{2*5}=\frac{25+\sqrt{685}}{10}
$