5y^2+34y-1=0

Solution for 5y^2+34y-1=0 equation:

5y^2+34y-1=0

a = 5; b = 34; c = -1;
Δ = b2-4ac
Δ = 342-4·5·(-1)
Δ = 1176
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:

$\sqrt{\Delta}=\sqrt{1176}=\sqrt{196*6}=\sqrt{196}*\sqrt{6}=14\sqrt{6}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-14\sqrt{6}}{2*5}=\frac{-34-14\sqrt{6}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+14\sqrt{6}}{2*5}=\frac{-34+14\sqrt{6}}{10}
$