50(1-x^2)-75x=0

Solution for 50(1-x^2)-75x=0 equation:

50(1-x^2)-75x=0

We multiply parentheses

-50x^2-75x+50=0

a = -50; b = -75; c = +50;
Δ = b2-4ac
Δ = -752-4·(-50)·50
Δ = 15625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{15625}=125$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-75)-125}{2*-50}=\frac{-50}{-100}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+125}{2*-50}=\frac{200}{-100}
=-2
$