Y=4x^2-9-3

Solution for Y=4x^2-9-3 equation:

=4Y^2-9-3

We move all terms to the left:

-(4Y^2-9-3)=0

We get rid of parentheses

-4Y^2+9+3=0

We add all the numbers together, and all the variables

-4Y^2+12=0

a = -4; b = 0; c = +12;
Δ = b2-4ac
Δ = 02-4·(-4)·12
Δ = 192
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:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{3}}{2*-4}=\frac{0-8\sqrt{3}}{-8}
=-\frac{8\sqrt{3}}{-8}
=-\frac{\sqrt{3}}{-1}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{3}}{2*-4}=\frac{0+8\sqrt{3}}{-8}
=\frac{8\sqrt{3}}{-8}
=\frac{\sqrt{3}}{-1}
$