51x-x^2-550=0

Solution for 51x-x^2-550=0 equation:

51x-x^2-550=0

We add all the numbers together, and all the variables

-1x^2+51x-550=0

a = -1; b = 51; c = -550;
Δ = b2-4ac
Δ = 512-4·(-1)·(-550)
Δ = 401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(51)-\sqrt{401}}{2*-1}=\frac{-51-\sqrt{401}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+\sqrt{401}}{2*-1}=\frac{-51+\sqrt{401}}{-2}
$