40b^2-40b-64=0

Solution for 40b^2-40b-64=0 equation:

40b^2-40b-64=0

a = 40; b = -40; c = -64;
Δ = b2-4ac
Δ = -402-4·40·(-64)
Δ = 11840
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{11840}=\sqrt{64*185}=\sqrt{64}*\sqrt{185}=8\sqrt{185}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-8\sqrt{185}}{2*40}=\frac{40-8\sqrt{185}}{80}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+8\sqrt{185}}{2*40}=\frac{40+8\sqrt{185}}{80}
$