8x-16/x+5=0

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Solution for 8x-16/x+5=0 equation: 



8x-16/x+5=0



Domain of the equation: x!=0

x∈R



We multiply all the terms by the denominator


8x*x+5*x-16=0

We add all the numbers together, and all the variables

5x+8x*x-16=0

Wy multiply elements

8x^2+5x-16=0

a = 8; b = 5; c = -16;
Δ = b2-4ac
Δ = 52-4·8·(-16)
Δ = 537
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{-(5)-\sqrt{537}}{2*8}=\frac{-5-\sqrt{537}}{16}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{537}}{2*8}=\frac{-5+\sqrt{537}}{16}
$

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