(1.25x)x=1000

Solution for (1.25x)x=1000 equation:

(1.25x)x=1000

We move all terms to the left:

(1.25x)x-(1000)=0

We add all the numbers together, and all the variables

(+1.25x)x-1000=0

We multiply parentheses

x^2-1000=0

a = 1; b = 0; c = -1000;
Δ = b2-4ac
Δ = 02-4·1·(-1000)
Δ = 4000
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:

$\sqrt{\Delta}=\sqrt{4000}=\sqrt{400*10}=\sqrt{400}*\sqrt{10}=20\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{10}}{2*1}=\frac{0-20\sqrt{10}}{2}
=-\frac{20\sqrt{10}}{2}
=-10\sqrt{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{10}}{2*1}=\frac{0+20\sqrt{10}}{2}
=\frac{20\sqrt{10}}{2}
=10\sqrt{10}
$