2y^2+34y=104

Solution for 2y^2+34y=104 equation:

2y^2+34y=104

We move all terms to the left:

2y^2+34y-(104)=0

a = 2; b = 34; c = -104;
Δ = b2-4ac
Δ = 342-4·2·(-104)
Δ = 1988
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:

$\sqrt{\Delta}=\sqrt{1988}=\sqrt{4*497}=\sqrt{4}*\sqrt{497}=2\sqrt{497}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-2\sqrt{497}}{2*2}=\frac{-34-2\sqrt{497}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+2\sqrt{497}}{2*2}=\frac{-34+2\sqrt{497}}{4}
$