Y=3x^2-18x+2

Solution for Y=3x^2-18x+2 equation:

=3Y^2-18Y+2

We move all terms to the left:

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

We get rid of parentheses

-3Y^2+18Y-2=0

a = -3; b = 18; c = -2;
Δ = b2-4ac
Δ = 182-4·(-3)·(-2)
Δ = 300
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:

$\sqrt{\Delta}=\sqrt{300}=\sqrt{100*3}=\sqrt{100}*\sqrt{3}=10\sqrt{3}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-10\sqrt{3}}{2*-3}=\frac{-18-10\sqrt{3}}{-6}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+10\sqrt{3}}{2*-3}=\frac{-18+10\sqrt{3}}{-6}
$