40y^2-40y-50=0

Solution for 40y^2-40y-50=0 equation:

40y^2-40y-50=0

a = 40; b = -40; c = -50;
Δ = b2-4ac
Δ = -402-4·40·(-50)
Δ = 9600
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:

$\sqrt{\Delta}=\sqrt{9600}=\sqrt{1600*6}=\sqrt{1600}*\sqrt{6}=40\sqrt{6}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-40\sqrt{6}}{2*40}=\frac{40-40\sqrt{6}}{80}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+40\sqrt{6}}{2*40}=\frac{40+40\sqrt{6}}{80}
$