5y^2-8y-128=0

Solution for 5y^2-8y-128=0 equation:

5y^2-8y-128=0

a = 5; b = -8; c = -128;
Δ = b2-4ac
Δ = -82-4·5·(-128)
Δ = 2624
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:

$\sqrt{\Delta}=\sqrt{2624}=\sqrt{64*41}=\sqrt{64}*\sqrt{41}=8\sqrt{41}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8\sqrt{41}}{2*5}=\frac{8-8\sqrt{41}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8\sqrt{41}}{2*5}=\frac{8+8\sqrt{41}}{10}
$