Y=x^2-19

Solution for Y=x^2-19 equation:

=Y^2-19

We move all terms to the left:

-(Y^2-19)=0

We get rid of parentheses

-Y^2+19=0

We add all the numbers together, and all the variables

-1Y^2+19=0

a = -1; b = 0; c = +19;
Δ = b2-4ac
Δ = 02-4·(-1)·19
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{19}}{2*-1}=\frac{0-2\sqrt{19}}{-2}
=-\frac{2\sqrt{19}}{-2}
=-\frac{\sqrt{19}}{-1}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{19}}{2*-1}=\frac{0+2\sqrt{19}}{-2}
=\frac{2\sqrt{19}}{-2}
=\frac{\sqrt{19}}{-1}
$