2,5x-250/x-5=0

Solution for 2,5x-250/x-5=0 equation:

2.5x-250/x-5=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


(2.5x)*x-5*x-250=0

We add all the numbers together, and all the variables

(+2.5x)*x-5*x-250=0

We add all the numbers together, and all the variables

-5x+(+2.5x)*x-250=0

We multiply parentheses

2x^2-5x-250=0

a = 2; b = -5; c = -250;
Δ = b2-4ac
Δ = -52-4·2·(-250)
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-45}{2*2}=\frac{-40}{4}
=-10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+45}{2*2}=\frac{50}{4}
=12+1/2
$