Y=-5x^2+20x-15

Solution for Y=-5x^2+20x-15 equation:

=-5Y^2+20Y-15

We move all terms to the left:

-(-5Y^2+20Y-15)=0

We get rid of parentheses

5Y^2-20Y+15=0

a = 5; b = -20; c = +15;
Δ = b2-4ac
Δ = -202-4·5·15
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-10}{2*5}=\frac{10}{10}
=1
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+10}{2*5}=\frac{30}{10}
=3
$