4x-8/x+5=0

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

4x-8/x+5=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

5x+4x*x-8=0

Wy multiply elements

4x^2+5x-8=0

a = 4; b = 5; c = -8;
Δ = b2-4ac
Δ = 52-4·4·(-8)
Δ = 153
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:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-3\sqrt{17}}{2*4}=\frac{-5-3\sqrt{17}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+3\sqrt{17}}{2*4}=\frac{-5+3\sqrt{17}}{8}
$