Y=x2-4x-28

Solution for Y=x2-4x-28 equation:

=Y2-4Y-28

We move all terms to the left:

-(Y2-4Y-28)=0

We add all the numbers together, and all the variables

-(+Y^2-4Y-28)=0

We get rid of parentheses

-Y^2+4Y+28=0

We add all the numbers together, and all the variables

-1Y^2+4Y+28=0

a = -1; b = 4; c = +28;
Δ = b2-4ac
Δ = 42-4·(-1)·28
Δ = 128
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{128}=\sqrt{64*2}=\sqrt{64}*\sqrt{2}=8\sqrt{2}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-8\sqrt{2}}{2*-1}=\frac{-4-8\sqrt{2}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+8\sqrt{2}}{2*-1}=\frac{-4+8\sqrt{2}}{-2}
$