x(2x-250)=2858

Solution for x(2x-250)=2858 equation:

x(2x-250)=2858

We move all terms to the left:

x(2x-250)-(2858)=0

We multiply parentheses

2x^2-250x-2858=0

a = 2; b = -250; c = -2858;
Δ = b2-4ac
Δ = -2502-4·2·(-2858)
Δ = 85364
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:

$\sqrt{\Delta}=\sqrt{85364}=\sqrt{4*21341}=\sqrt{4}*\sqrt{21341}=2\sqrt{21341}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-250)-2\sqrt{21341}}{2*2}=\frac{250-2\sqrt{21341}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-250)+2\sqrt{21341}}{2*2}=\frac{250+2\sqrt{21341}}{4}
$