3/7x=7-x

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



3/7x=7-x

We move all terms to the left:

3/7x-(7-x)=0



Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



We add all the numbers together, and all the variables

3/7x-(-1x+7)=0

We get rid of parentheses

3/7x+1x-7=0

We multiply all the terms by the denominator


1x*7x-7*7x+3=0

Wy multiply elements

7x^2-49x+3=0

a = 7; b = -49; c = +3;
Δ = b2-4ac
Δ = -492-4·7·3
Δ = 2317
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{-(-49)-\sqrt{2317}}{2*7}=\frac{49-\sqrt{2317}}{14}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-49)+\sqrt{2317}}{2*7}=\frac{49+\sqrt{2317}}{14}
$

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