Y=2x2+12x+14

Solution for Y=2x2+12x+14 equation:

=2Y^2+12Y+14

We move all terms to the left:

-(2Y^2+12Y+14)=0

We get rid of parentheses

-2Y^2-12Y-14=0

a = -2; b = -12; c = -14;
Δ = b2-4ac
Δ = -122-4·(-2)·(-14)
Δ = 32
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:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{2}}{2*-2}=\frac{12-4\sqrt{2}}{-4}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{2}}{2*-2}=\frac{12+4\sqrt{2}}{-4}
$