Y=-3x^2+21x+6

Solution for Y=-3x^2+21x+6 equation:

=-3Y^2+21Y+6

We move all terms to the left:

-(-3Y^2+21Y+6)=0

We get rid of parentheses

3Y^2-21Y-6=0

a = 3; b = -21; c = -6;
Δ = b2-4ac
Δ = -212-4·3·(-6)
Δ = 513
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:

$\sqrt{\Delta}=\sqrt{513}=\sqrt{9*57}=\sqrt{9}*\sqrt{57}=3\sqrt{57}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-3\sqrt{57}}{2*3}=\frac{21-3\sqrt{57}}{6}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+3\sqrt{57}}{2*3}=\frac{21+3\sqrt{57}}{6}
$