Y=2x2-12x+17

Solution for Y=2x2-12x+17 equation:

=2Y^2-12Y+17

We move all terms to the left:

-(2Y^2-12Y+17)=0

We get rid of parentheses

-2Y^2+12Y-17=0

a = -2; b = 12; c = -17;
Δ = b2-4ac
Δ = 122-4·(-2)·(-17)
Δ = 8
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:

$\sqrt{\Delta}=\sqrt{8}=\sqrt{4*2}=\sqrt{4}*\sqrt{2}=2\sqrt{2}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{2}}{2*-2}=\frac{-12-2\sqrt{2}}{-4}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{2}}{2*-2}=\frac{-12+2\sqrt{2}}{-4}
$