Y=2x^2-18x+6

Solution for Y=2x^2-18x+6 equation:

=2Y^2-18Y+6

We move all terms to the left:

-(2Y^2-18Y+6)=0

We get rid of parentheses

-2Y^2+18Y-6=0

a = -2; b = 18; c = -6;
Δ = b2-4ac
Δ = 182-4·(-2)·(-6)
Δ = 276
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:

$\sqrt{\Delta}=\sqrt{276}=\sqrt{4*69}=\sqrt{4}*\sqrt{69}=2\sqrt{69}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{69}}{2*-2}=\frac{-18-2\sqrt{69}}{-4}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{69}}{2*-2}=\frac{-18+2\sqrt{69}}{-4}
$