Y=0.5x^2-5x-3

Solution for Y=0.5x^2-5x-3 equation:

=0.5Y^2-5Y-3

We move all terms to the left:

-(0.5Y^2-5Y-3)=0

We get rid of parentheses

-0.5Y^2+5Y+3=0

a = -0.5; b = 5; c = +3;
Δ = b2-4ac
Δ = 52-4·(-0.5)·3
Δ = 31
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{31}}{2*-0.5}=\frac{-5-\sqrt{31}}{-1}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{31}}{2*-0.5}=\frac{-5+\sqrt{31}}{-1}
$