1050=50x-0.5x2

Solution for 1050=50x-0.5x2 equation:

1050=50x-0.5x^2

We move all terms to the left:

1050-(50x-0.5x^2)=0

We get rid of parentheses

0.5x^2-50x+1050=0

a = 0.5; b = -50; c = +1050;
Δ = b2-4ac
Δ = -502-4·0.5·1050
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-20}{2*0.5}=\frac{30}{1}
=30
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+20}{2*0.5}=\frac{70}{1}
=70
$