4x-1/x=x+7

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Solution for 4x-1/x=x+7 equation:



4x-1/x=x+7
We move all terms to the left:
4x-1/x-(x+7)=0
Domain of the equation: x!=0
x∈R
We get rid of parentheses
4x-1/x-x-7=0
We multiply all the terms by the denominator
4x*x-x*x-7*x-1=0
We add all the numbers together, and all the variables
-7x+4x*x-x*x-1=0
Wy multiply elements
4x^2-1x^2-7x-1=0
We add all the numbers together, and all the variables
3x^2-7x-1=0
a = 3; b = -7; c = -1;
Δ = b2-4ac
Δ = -72-4·3·(-1)
Δ = 61
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{-(-7)-\sqrt{61}}{2*3}=\frac{7-\sqrt{61}}{6} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{61}}{2*3}=\frac{7+\sqrt{61}}{6} $

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