Y=7x^2-19

Solution for Y=7x^2-19 equation:

=7Y^2-19

We move all terms to the left:

-(7Y^2-19)=0

We get rid of parentheses

-7Y^2+19=0

a = -7; b = 0; c = +19;
Δ = b2-4ac
Δ = 02-4·(-7)·19
Δ = 532
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:

$\sqrt{\Delta}=\sqrt{532}=\sqrt{4*133}=\sqrt{4}*\sqrt{133}=2\sqrt{133}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{133}}{2*-7}=\frac{0-2\sqrt{133}}{-14}
=-\frac{2\sqrt{133}}{-14}
=-\frac{\sqrt{133}}{-7}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{133}}{2*-7}=\frac{0+2\sqrt{133}}{-14}
=\frac{2\sqrt{133}}{-14}
=\frac{\sqrt{133}}{-7}
$