a^2-40a-1375=0

Solution for a^2-40a-1375=0 equation:

a^2-40a-1375=0

a = 1; b = -40; c = -1375;
Δ = b2-4ac
Δ = -402-4·1·(-1375)
Δ = 7100
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:

$\sqrt{\Delta}=\sqrt{7100}=\sqrt{100*71}=\sqrt{100}*\sqrt{71}=10\sqrt{71}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-10\sqrt{71}}{2*1}=\frac{40-10\sqrt{71}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+10\sqrt{71}}{2*1}=\frac{40+10\sqrt{71}}{2}
$