Y=x^2-8x-19

Solution for Y=x^2-8x-19 equation:

=Y^2-8Y-19

We move all terms to the left:

-(Y^2-8Y-19)=0

We get rid of parentheses

-Y^2+8Y+19=0

We add all the numbers together, and all the variables

-1Y^2+8Y+19=0

a = -1; b = 8; c = +19;
Δ = b2-4ac
Δ = 82-4·(-1)·19
Δ = 140
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:

$\sqrt{\Delta}=\sqrt{140}=\sqrt{4*35}=\sqrt{4}*\sqrt{35}=2\sqrt{35}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{35}}{2*-1}=\frac{-8-2\sqrt{35}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{35}}{2*-1}=\frac{-8+2\sqrt{35}}{-2}
$