40a^2-64=0

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

40a^2-64=0

a = 40; b = 0; c = -64;
Δ = b2-4ac
Δ = 02-4·40·(-64)
Δ = 10240
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{10240}=\sqrt{1024*10}=\sqrt{1024}*\sqrt{10}=32\sqrt{10}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-32\sqrt{10}}{2*40}=\frac{0-32\sqrt{10}}{80}
=-\frac{32\sqrt{10}}{80}
=-\frac{2\sqrt{10}}{5}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+32\sqrt{10}}{2*40}=\frac{0+32\sqrt{10}}{80}
=\frac{32\sqrt{10}}{80}
=\frac{2\sqrt{10}}{5}
$