50(1-x^2)-25x-50=0

Solution for 50(1-x^2)-25x-50=0 equation:

50(1-x^2)-25x-50=0

We multiply parentheses

-50x^2-25x+50-50=0

We add all the numbers together, and all the variables

-50x^2-25x=0

a = -50; b = -25; c = 0;
Δ = b2-4ac
Δ = -252-4·(-50)·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-25}{2*-50}=\frac{0}{-100}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+25}{2*-50}=\frac{50}{-100}
=-1/2
$