Y=-0.5x^2+5x-8

Solution for Y=-0.5x^2+5x-8 equation:

=-0.5Y^2+5Y-8

We move all terms to the left:

-(-0.5Y^2+5Y-8)=0

We get rid of parentheses

0.5Y^2-5Y+8=0

a = 0.5; b = -5; c = +8;
Δ = b2-4ac
Δ = -52-4·0.5·8
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-3}{2*0.5}=\frac{2}{1}
=2
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+3}{2*0.5}=\frac{8}{1}
=8
$