x-2.5-9/x=0

Solution for x-2.5-9/x=0 equation:

x-2.5-9/x=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


x*x-(2.5)*x-9=0

We multiply parentheses

x*x-2.5x-9=0

Wy multiply elements

x^2-2.5x-9=0

a = 1; b = -2.5; c = -9;
Δ = b2-4ac
Δ = -2.52-4·1·(-9)
Δ = 42.25
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{42.25}}{2*1}=\frac{2.5-\sqrt{42.25}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2.5)+\sqrt{42.25}}{2*1}=\frac{2.5+\sqrt{42.25}}{2}
$