50x+400=100x-x^2

Solution for 50x+400=100x-x^2 equation:

50x+400=100x-x^2

We move all terms to the left:

50x+400-(100x-x^2)=0

We get rid of parentheses

x^2-100x+50x+400=0

We add all the numbers together, and all the variables

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