19=y2-16

Solution for 19=y2-16 equation:

19=y2-16

We move all terms to the left:

19-(y2-16)=0

We add all the numbers together, and all the variables

-(+y^2-16)+19=0

We get rid of parentheses

-y^2+16+19=0

We add all the numbers together, and all the variables

-1y^2+35=0

a = -1; b = 0; c = +35;
Δ = b2-4ac
Δ = 02-4·(-1)·35
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{-(0)-2\sqrt{35}}{2*-1}=\frac{0-2\sqrt{35}}{-2}
=-\frac{2\sqrt{35}}{-2}
=-\frac{\sqrt{35}}{-1}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{35}}{2*-1}=\frac{0+2\sqrt{35}}{-2}
=\frac{2\sqrt{35}}{-2}
=\frac{\sqrt{35}}{-1}
$