x*(2.5*x)=250

Solution for x*(2.5*x)=250 equation:

x(2.5x)=250

We move all terms to the left:

x(2.5x)-(250)=0

We add all the numbers together, and all the variables

x(+2.5x)-250=0

We multiply parentheses

2x^2-250=0

a = 2; b = 0; c = -250;
Δ = b2-4ac
Δ = 02-4·2·(-250)
Δ = 2000
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:

$\sqrt{\Delta}=\sqrt{2000}=\sqrt{400*5}=\sqrt{400}*\sqrt{5}=20\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{5}}{2*2}=\frac{0-20\sqrt{5}}{4}
=-\frac{20\sqrt{5}}{4}
=-5\sqrt{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{5}}{2*2}=\frac{0+20\sqrt{5}}{4}
=\frac{20\sqrt{5}}{4}
=5\sqrt{5}
$