Y=3x2-9x+5

Solution for Y=3x2-9x+5 equation:

=3Y^2-9Y+5

We move all terms to the left:

-(3Y^2-9Y+5)=0

We get rid of parentheses

-3Y^2+9Y-5=0

a = -3; b = 9; c = -5;
Δ = b2-4ac
Δ = 92-4·(-3)·(-5)
Δ = 21
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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