25x=100+x-x*x

Solution for 25x=100+x-x*x equation:

25x=100+x-x*x

We move all terms to the left:

25x-(100+x-x*x)=0

We add all the numbers together, and all the variables

25x-(x-x*x+100)=0

We get rid of parentheses

25x-x+x*x-100=0

We add all the numbers together, and all the variables

24x+x*x-100=0

Wy multiply elements

x^2+24x-100=0

a = 1; b = 24; c = -100;
Δ = b2-4ac
Δ = 242-4·1·(-100)
Δ = 976
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{976}=\sqrt{16*61}=\sqrt{16}*\sqrt{61}=4\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{61}}{2*1}=\frac{-24-4\sqrt{61}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{61}}{2*1}=\frac{-24+4\sqrt{61}}{2}
$