Y=x2-3x-4

Solution for Y=x2-3x-4 equation:

=Y2-3Y-4

We move all terms to the left:

-(Y2-3Y-4)=0

We add all the numbers together, and all the variables

-(+Y^2-3Y-4)=0

We get rid of parentheses

-Y^2+3Y+4=0

We add all the numbers together, and all the variables

-1Y^2+3Y+4=0

a = -1; b = 3; c = +4;
Δ = b2-4ac
Δ = 32-4·(-1)·4
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-5}{2*-1}=\frac{-8}{-2}
=+4
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+5}{2*-1}=\frac{2}{-2}
=-1
$