61x-x^2=550

Solution for 61x-x^2=550 equation:

61x-x^2=550

We move all terms to the left:

61x-x^2-(550)=0

We add all the numbers together, and all the variables

-1x^2+61x-550=0

a = -1; b = 61; c = -550;
Δ = b2-4ac
Δ = 612-4·(-1)·(-550)
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(61)-39}{2*-1}=\frac{-100}{-2}
=+50
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(61)+39}{2*-1}=\frac{-22}{-2}
=+11
$