2x-80/x=5

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Solution for 2x-80/x=5 equation:



2x-80/x=5
We move all terms to the left:
2x-80/x-(5)=0
Domain of the equation: x!=0
x∈R
We multiply all the terms by the denominator
2x*x-5*x-80=0
We add all the numbers together, and all the variables
-5x+2x*x-80=0
Wy multiply elements
2x^2-5x-80=0
a = 2; b = -5; c = -80;
Δ = b2-4ac
Δ = -52-4·2·(-80)
Δ = 665
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{665}}{2*2}=\frac{5-\sqrt{665}}{4} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{665}}{2*2}=\frac{5+\sqrt{665}}{4} $

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