110x^-x^2=2500

Solution for 110x^-x^2=2500 equation:

110x^-x^2=2500

We move all terms to the left:

110x^-x^2-(2500)=0

We add all the numbers together, and all the variables

-1x^2+110x-2500=0

a = -1; b = 110; c = -2500;
Δ = b2-4ac
Δ = 1102-4·(-1)·(-2500)
Δ = 2100
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:

$\sqrt{\Delta}=\sqrt{2100}=\sqrt{100*21}=\sqrt{100}*\sqrt{21}=10\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(110)-10\sqrt{21}}{2*-1}=\frac{-110-10\sqrt{21}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(110)+10\sqrt{21}}{2*-1}=\frac{-110+10\sqrt{21}}{-2}
$