Y=19x^2-21

Solution for Y=19x^2-21 equation:

=19Y^2-21

We move all terms to the left:

-(19Y^2-21)=0

We get rid of parentheses

-19Y^2+21=0

a = -19; b = 0; c = +21;
Δ = b2-4ac
Δ = 02-4·(-19)·21
Δ = 1596
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:

$\sqrt{\Delta}=\sqrt{1596}=\sqrt{4*399}=\sqrt{4}*\sqrt{399}=2\sqrt{399}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{399}}{2*-19}=\frac{0-2\sqrt{399}}{-38}
=-\frac{2\sqrt{399}}{-38}
=-\frac{\sqrt{399}}{-19}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{399}}{2*-19}=\frac{0+2\sqrt{399}}{-38}
=\frac{2\sqrt{399}}{-38}
=\frac{\sqrt{399}}{-19}
$