Y=2x^2+122x+18

Solution for Y=2x^2+122x+18 equation:

=2Y^2+122Y+18

We move all terms to the left:

-(2Y^2+122Y+18)=0

We get rid of parentheses

-2Y^2-122Y-18=0

a = -2; b = -122; c = -18;
Δ = b2-4ac
Δ = -1222-4·(-2)·(-18)
Δ = 14740
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:

$\sqrt{\Delta}=\sqrt{14740}=\sqrt{4*3685}=\sqrt{4}*\sqrt{3685}=2\sqrt{3685}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-122)-2\sqrt{3685}}{2*-2}=\frac{122-2\sqrt{3685}}{-4}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-122)+2\sqrt{3685}}{2*-2}=\frac{122+2\sqrt{3685}}{-4}
$