Y=X^2-6x-11.25

Solution for Y=X^2-6x-11.25 equation:

=Y^2-6Y-11.25

We move all terms to the left:

-(Y^2-6Y-11.25)=0

We get rid of parentheses

-Y^2+6Y+11.25=0

We add all the numbers together, and all the variables

-1Y^2+6Y+11.25=0

a = -1; b = 6; c = +11.25;
Δ = b2-4ac
Δ = 62-4·(-1)·11.25
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-9}{2*-1}=\frac{-15}{-2}
=7+1/2
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+9}{2*-1}=\frac{3}{-2}
=-1+1/2
$