50x-x^2=624

Solution for 50x-x^2=624 equation:

50x-x^2=624

We move all terms to the left:

50x-x^2-(624)=0

We add all the numbers together, and all the variables

-1x^2+50x-624=0

a = -1; b = 50; c = -624;
Δ = b2-4ac
Δ = 502-4·(-1)·(-624)
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-2}{2*-1}=\frac{-52}{-2}
=+26
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+2}{2*-1}=\frac{-48}{-2}
=+24
$