Y=x2-5x-24

Solution for Y=x2-5x-24 equation:

=Y2-5Y-24

We move all terms to the left:

-(Y2-5Y-24)=0

We add all the numbers together, and all the variables

-(+Y^2-5Y-24)=0

We get rid of parentheses

-Y^2+5Y+24=0

We add all the numbers together, and all the variables

-1Y^2+5Y+24=0

a = -1; b = 5; c = +24;
Δ = b2-4ac
Δ = 52-4·(-1)·24
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-11}{2*-1}=\frac{-16}{-2}
=+8
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+11}{2*-1}=\frac{6}{-2}
=-3
$