5x-8/x-4=0

Solution for 5x-8/x-4=0 equation:

5x-8/x-4=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


5x*x-4*x-8=0

We add all the numbers together, and all the variables

-4x+5x*x-8=0

Wy multiply elements

5x^2-4x-8=0

a = 5; b = -4; c = -8;
Δ = b2-4ac
Δ = -42-4·5·(-8)
Δ = 176
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:

$\sqrt{\Delta}=\sqrt{176}=\sqrt{16*11}=\sqrt{16}*\sqrt{11}=4\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{11}}{2*5}=\frac{4-4\sqrt{11}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{11}}{2*5}=\frac{4+4\sqrt{11}}{10}
$