9y^2-2y-8=0

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

9y^2-2y-8=0

a = 9; b = -2; c = -8;
Δ = b2-4ac
Δ = -22-4·9·(-8)
Δ = 292
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:

$\sqrt{\Delta}=\sqrt{292}=\sqrt{4*73}=\sqrt{4}*\sqrt{73}=2\sqrt{73}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{73}}{2*9}=\frac{2-2\sqrt{73}}{18}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{73}}{2*9}=\frac{2+2\sqrt{73}}{18}
$