Y=x^2-2.5x-6

Solution for Y=x^2-2.5x-6 equation:

=Y^2-2.5Y-6

We move all terms to the left:

-(Y^2-2.5Y-6)=0

We get rid of parentheses

-Y^2+2.5Y+6=0

We add all the numbers together, and all the variables

-1Y^2+2.5Y+6=0

a = -1; b = 2.5; c = +6;
Δ = b2-4ac
Δ = 2.52-4·(-1)·6
Δ = 30.25
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{-(2.5)-\sqrt{30.25}}{2*-1}=\frac{-2.5-\sqrt{30.25}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2.5)+\sqrt{30.25}}{2*-1}=\frac{-2.5+\sqrt{30.25}}{-2}
$