29x-x^2=204

Solution for 29x-x^2=204 equation:

29x-x^2=204

We move all terms to the left:

29x-x^2-(204)=0

We add all the numbers together, and all the variables

-1x^2+29x-204=0

a = -1; b = 29; c = -204;
Δ = b2-4ac
Δ = 292-4·(-1)·(-204)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-5}{2*-1}=\frac{-34}{-2}
=+17
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+5}{2*-1}=\frac{-24}{-2}
=+12
$