2y2-34y-14=0

Solution for 2y2-34y-14=0 equation:

2y^2-34y-14=0

a = 2; b = -34; c = -14;
Δ = b2-4ac
Δ = -342-4·2·(-14)
Δ = 1268
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:

$\sqrt{\Delta}=\sqrt{1268}=\sqrt{4*317}=\sqrt{4}*\sqrt{317}=2\sqrt{317}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2\sqrt{317}}{2*2}=\frac{34-2\sqrt{317}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2\sqrt{317}}{2*2}=\frac{34+2\sqrt{317}}{4}
$