x(2x-10)=1000

Solution for x(2x-10)=1000 equation:

x(2x-10)=1000

We move all terms to the left:

x(2x-10)-(1000)=0

We multiply parentheses

2x^2-10x-1000=0

a = 2; b = -10; c = -1000;
Δ = b2-4ac
Δ = -102-4·2·(-1000)
Δ = 8100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8100}=90$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-90}{2*2}=\frac{-80}{4}
=-20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+90}{2*2}=\frac{100}{4}
=25
$