5y^2+8y-34=0

Solution for 5y^2+8y-34=0 equation:

5y^2+8y-34=0

a = 5; b = 8; c = -34;
Δ = b2-4ac
Δ = 82-4·5·(-34)
Δ = 744
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:

$\sqrt{\Delta}=\sqrt{744}=\sqrt{4*186}=\sqrt{4}*\sqrt{186}=2\sqrt{186}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{186}}{2*5}=\frac{-8-2\sqrt{186}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{186}}{2*5}=\frac{-8+2\sqrt{186}}{10}
$