x(x-2.5)=800

Solution for x(x-2.5)=800 equation:

x(x-2.5)=800

We move all terms to the left:

x(x-2.5)-(800)=0

We multiply parentheses

x^2-2.5x-800=0

a = 1; b = -2.5; c = -800;
Δ = b2-4ac
Δ = -2.52-4·1·(-800)
Δ = 3206.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2.5)-\sqrt{3206.25}}{2*1}=\frac{2.5-\sqrt{3206.25}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2.5)+\sqrt{3206.25}}{2*1}=\frac{2.5+\sqrt{3206.25}}{2}
$