1/x=7-3x

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Solution for 1/x=7-3x equation:



1/x=7-3x
We move all terms to the left:
1/x-(7-3x)=0
Domain of the equation: x!=0
x∈R
We add all the numbers together, and all the variables
1/x-(-3x+7)=0
We get rid of parentheses
1/x+3x-7=0
We multiply all the terms by the denominator
3x*x-7*x+1=0
We add all the numbers together, and all the variables
-7x+3x*x+1=0
Wy multiply elements
3x^2-7x+1=0
a = 3; b = -7; c = +1;
Δ = b2-4ac
Δ = -72-4·3·1
Δ = 37
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{37}}{2*3}=\frac{7-\sqrt{37}}{6} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{37}}{2*3}=\frac{7+\sqrt{37}}{6} $

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