Y=-4x2+6

Solution for Y=-4x2+6 equation:

=-4Y^2+6

We move all terms to the left:

-(-4Y^2+6)=0

We get rid of parentheses

4Y^2-6=0

a = 4; b = 0; c = -6;
Δ = b2-4ac
Δ = 02-4·4·(-6)
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{6}}{2*4}=\frac{0-4\sqrt{6}}{8}
=-\frac{4\sqrt{6}}{8}
=-\frac{\sqrt{6}}{2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{6}}{2*4}=\frac{0+4\sqrt{6}}{8}
=\frac{4\sqrt{6}}{8}
=\frac{\sqrt{6}}{2}
$