Y=-4x^2+6x+2

Solution for Y=-4x^2+6x+2 equation:

=-4Y^2+6Y+2

We move all terms to the left:

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

We get rid of parentheses

4Y^2-6Y-2=0

a = 4; b = -6; c = -2;
Δ = b2-4ac
Δ = -62-4·4·(-2)
Δ = 68
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:

$\sqrt{\Delta}=\sqrt{68}=\sqrt{4*17}=\sqrt{4}*\sqrt{17}=2\sqrt{17}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{17}}{2*4}=\frac{6-2\sqrt{17}}{8}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{17}}{2*4}=\frac{6+2\sqrt{17}}{8}
$