5a^2-40a-80=0

Solution for 5a^2-40a-80=0 equation:

5a^2-40a-80=0

a = 5; b = -40; c = -80;
Δ = b2-4ac
Δ = -402-4·5·(-80)
Δ = 3200
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:

$\sqrt{\Delta}=\sqrt{3200}=\sqrt{1600*2}=\sqrt{1600}*\sqrt{2}=40\sqrt{2}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-40\sqrt{2}}{2*5}=\frac{40-40\sqrt{2}}{10}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+40\sqrt{2}}{2*5}=\frac{40+40\sqrt{2}}{10}
$