40x-x^2-375=0

Solution for 40x-x^2-375=0 equation:

40x-x^2-375=0

We add all the numbers together, and all the variables

-1x^2+40x-375=0

a = -1; b = 40; c = -375;
Δ = b2-4ac
Δ = 402-4·(-1)·(-375)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-10}{2*-1}=\frac{-50}{-2}
=+25
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+10}{2*-1}=\frac{-30}{-2}
=+15
$