29x-x^2-100=0

Solution for 29x-x^2-100=0 equation:

29x-x^2-100=0

We add all the numbers together, and all the variables

-1x^2+29x-100=0

a = -1; b = 29; c = -100;
Δ = b2-4ac
Δ = 292-4·(-1)·(-100)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-21}{2*-1}=\frac{-50}{-2}
=+25
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+21}{2*-1}=\frac{-8}{-2}
=+4
$