9y^2-40y-16=0

Solution for 9y^2-40y-16=0 equation:

9y^2-40y-16=0

a = 9; b = -40; c = -16;
Δ = b2-4ac
Δ = -402-4·9·(-16)
Δ = 2176
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:

$\sqrt{\Delta}=\sqrt{2176}=\sqrt{64*34}=\sqrt{64}*\sqrt{34}=8\sqrt{34}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-8\sqrt{34}}{2*9}=\frac{40-8\sqrt{34}}{18}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+8\sqrt{34}}{2*9}=\frac{40+8\sqrt{34}}{18}
$