2y^2-5y-34=0

Solution for 2y^2-5y-34=0 equation:

2y^2-5y-34=0

a = 2; b = -5; c = -34;
Δ = b2-4ac
Δ = -52-4·2·(-34)
Δ = 297
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:

$\sqrt{\Delta}=\sqrt{297}=\sqrt{9*33}=\sqrt{9}*\sqrt{33}=3\sqrt{33}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-3\sqrt{33}}{2*2}=\frac{5-3\sqrt{33}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+3\sqrt{33}}{2*2}=\frac{5+3\sqrt{33}}{4}
$