2x-5/x=99

Solution for 2x-5/x=99 equation:

2x-5/x=99

We move all terms to the left:

2x-5/x-(99)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


2x*x-99*x-5=0

We add all the numbers together, and all the variables

-99x+2x*x-5=0

Wy multiply elements

2x^2-99x-5=0

a = 2; b = -99; c = -5;
Δ = b2-4ac
Δ = -992-4·2·(-5)
Δ = 9841
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{-(-99)-\sqrt{9841}}{2*2}=\frac{99-\sqrt{9841}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-99)+\sqrt{9841}}{2*2}=\frac{99+\sqrt{9841}}{4}
$