40-5a^2=0

Solution for 40-5a^2=0 equation:

40-5a^2=0

a = -5; b = 0; c = +40;
Δ = b2-4ac
Δ = 02-4·(-5)·40
Δ = 800
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:

$\sqrt{\Delta}=\sqrt{800}=\sqrt{400*2}=\sqrt{400}*\sqrt{2}=20\sqrt{2}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{2}}{2*-5}=\frac{0-20\sqrt{2}}{-10}
=-\frac{20\sqrt{2}}{-10}
=-\frac{2\sqrt{2}}{-1}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{2}}{2*-5}=\frac{0+20\sqrt{2}}{-10}
=\frac{20\sqrt{2}}{-10}
=\frac{2\sqrt{2}}{-1}
$