(2x-50)*x=1000

Solution for (2x-50)*x=1000 equation:

(2x-50)*x=1000

We move all terms to the left:

(2x-50)*x-(1000)=0

We multiply parentheses

2x^2-50x-1000=0

a = 2; b = -50; c = -1000;
Δ = b2-4ac
Δ = -502-4·2·(-1000)
Δ = 10500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{10500}=\sqrt{100*105}=\sqrt{100}*\sqrt{105}=10\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-10\sqrt{105}}{2*2}=\frac{50-10\sqrt{105}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+10\sqrt{105}}{2*2}=\frac{50+10\sqrt{105}}{4}
$