5y^2-8y-205=0

Solution for 5y^2-8y-205=0 equation:

5y^2-8y-205=0

a = 5; b = -8; c = -205;
Δ = b2-4ac
Δ = -82-4·5·(-205)
Δ = 4164
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:

$\sqrt{\Delta}=\sqrt{4164}=\sqrt{4*1041}=\sqrt{4}*\sqrt{1041}=2\sqrt{1041}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{1041}}{2*5}=\frac{8-2\sqrt{1041}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{1041}}{2*5}=\frac{8+2\sqrt{1041}}{10}
$