Y=3x2-11x+6

Solution for Y=3x2-11x+6 equation:

=3Y^2-11Y+6

We move all terms to the left:

-(3Y^2-11Y+6)=0

We get rid of parentheses

-3Y^2+11Y-6=0

a = -3; b = 11; c = -6;
Δ = b2-4ac
Δ = 112-4·(-3)·(-6)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-7}{2*-3}=\frac{-18}{-6}
=+3
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+7}{2*-3}=\frac{-4}{-6}
=2/3
$