Y=-3x2+18x-22

Solution for Y=-3x2+18x-22 equation:

=-3Y^2+18Y-22

We move all terms to the left:

-(-3Y^2+18Y-22)=0

We get rid of parentheses

3Y^2-18Y+22=0

a = 3; b = -18; c = +22;
Δ = b2-4ac
Δ = -182-4·3·22
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{15}}{2*3}=\frac{18-2\sqrt{15}}{6}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{15}}{2*3}=\frac{18+2\sqrt{15}}{6}
$