25x-x^2-100=0

Solution for 25x-x^2-100=0 equation:

25x-x^2-100=0

We add all the numbers together, and all the variables

-1x^2+25x-100=0

a = -1; b = 25; c = -100;
Δ = b2-4ac
Δ = 252-4·(-1)·(-100)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-15}{2*-1}=\frac{-40}{-2}
=+20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+15}{2*-1}=\frac{-10}{-2}
=+5
$