(x)/(7-x)=2x

Solution for (x)/(7-x)=2x equation:

(x)/(7-x)=2x

We move all terms to the left:

(x)/(7-x)-(2x)=0


Domain of the equation: (7-x)!=0

We move all terms containing x to the left, all other terms to the right

-x!=-7

x!=-7/-1

x!=+7

x∈R


We add all the numbers together, and all the variables

x/(-1x+7)-2x=0

We add all the numbers together, and all the variables

-2x+x/(-1x+7)=0

We multiply all the terms by the denominator


-2x*(-1x+7)+x=0

We add all the numbers together, and all the variables

x-2x*(-1x+7)=0

We multiply parentheses

2x^2+x-14x=0

We add all the numbers together, and all the variables

2x^2-13x=0

a = 2; b = -13; c = 0;
Δ = b2-4ac
Δ = -132-4·2·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-13}{2*2}=\frac{0}{4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+13}{2*2}=\frac{26}{4}
=6+1/2
$