40a-a^2=39

Solution for 40a-a^2=39 equation:

40a-a^2=39

We move all terms to the left:

40a-a^2-(39)=0

We add all the numbers together, and all the variables

-1a^2+40a-39=0

a = -1; b = 40; c = -39;
Δ = b2-4ac
Δ = 402-4·(-1)·(-39)
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-38}{2*-1}=\frac{-78}{-2}
=+39
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+38}{2*-1}=\frac{-2}{-2}
=1
$