Y2=4x2-9

Solution for Y2=4x2-9 equation:

2=4Y^2-9

We move all terms to the left:

2-(4Y^2-9)=0

We get rid of parentheses

-4Y^2+9+2=0

We add all the numbers together, and all the variables

-4Y^2+11=0

a = -4; b = 0; c = +11;
Δ = b2-4ac
Δ = 02-4·(-4)·11
Δ = 176
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:

$\sqrt{\Delta}=\sqrt{176}=\sqrt{16*11}=\sqrt{16}*\sqrt{11}=4\sqrt{11}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{11}}{2*-4}=\frac{0-4\sqrt{11}}{-8}
=-\frac{4\sqrt{11}}{-8}
=-\frac{\sqrt{11}}{-2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{11}}{2*-4}=\frac{0+4\sqrt{11}}{-8}
=\frac{4\sqrt{11}}{-8}
=\frac{\sqrt{11}}{-2}
$