50x-x^2=400

Solution for 50x-x^2=400 equation:

50x-x^2=400

We move all terms to the left:

50x-x^2-(400)=0

We add all the numbers together, and all the variables

-1x^2+50x-400=0

a = -1; b = 50; c = -400;
Δ = b2-4ac
Δ = 502-4·(-1)·(-400)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-30}{2*-1}=\frac{-80}{-2}
=+40
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+30}{2*-1}=\frac{-20}{-2}
=+10
$