5y^2+8y-9=0

Solution for 5y^2+8y-9=0 equation:

5y^2+8y-9=0

a = 5; b = 8; c = -9;
Δ = b2-4ac
Δ = 82-4·5·(-9)
Δ = 244
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:

$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{61}}{2*5}=\frac{-8-2\sqrt{61}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{61}}{2*5}=\frac{-8+2\sqrt{61}}{10}
$