65x-x^2=924

Solution for 65x-x^2=924 equation:

65x-x^2=924

We move all terms to the left:

65x-x^2-(924)=0

We add all the numbers together, and all the variables

-1x^2+65x-924=0

a = -1; b = 65; c = -924;
Δ = b2-4ac
Δ = 652-4·(-1)·(-924)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(65)-23}{2*-1}=\frac{-88}{-2}
=+44
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(65)+23}{2*-1}=\frac{-42}{-2}
=+21
$