2x-5/x-8=0

Solution for 2x-5/x-8=0 equation:

2x-5/x-8=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


2x*x-8*x-5=0

We add all the numbers together, and all the variables

-8x+2x*x-5=0

Wy multiply elements

2x^2-8x-5=0

a = 2; b = -8; c = -5;
Δ = b2-4ac
Δ = -82-4·2·(-5)
Δ = 104
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:

$\sqrt{\Delta}=\sqrt{104}=\sqrt{4*26}=\sqrt{4}*\sqrt{26}=2\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{26}}{2*2}=\frac{8-2\sqrt{26}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{26}}{2*2}=\frac{8+2\sqrt{26}}{4}
$