Y=0.5(x^2-6x)+2

Solution for Y=0.5(x^2-6x)+2 equation:

=0.5(Y^2-6Y)+2

We move all terms to the left:

-(0.5(Y^2-6Y)+2)=0


We calculate terms in parentheses: -(0.5(Y^2-6Y)+2), so:

0.5(Y^2-6Y)+2

We multiply parentheses

0.5Y^2-3Y+2

Back to the equation:

-(0.5Y^2-3Y+2)


We get rid of parentheses

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

a = -0.5; b = 3; c = -2;
Δ = b2-4ac
Δ = 32-4·(-0.5)·(-2)
Δ = 5
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{-(3)-\sqrt{5}}{2*-0.5}=\frac{-3-\sqrt{5}}{-1}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{5}}{2*-0.5}=\frac{-3+\sqrt{5}}{-1}
$