Y=-4x^2+11x-6

Solution for Y=-4x^2+11x-6 equation:

=-4Y^2+11Y-6

We move all terms to the left:

-(-4Y^2+11Y-6)=0

We get rid of parentheses

4Y^2-11Y+6=0

a = 4; b = -11; c = +6;
Δ = b2-4ac
Δ = -112-4·4·6
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-5}{2*4}=\frac{6}{8}
=3/4
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+5}{2*4}=\frac{16}{8}
=2
$