x=(3-x)11(3x)

Solution for x=(3-x)11(3x) equation:

x=(3-x)11(3x)

We move all terms to the left:

x-((3-x)11(3x))=0

We add all the numbers together, and all the variables

x-((-1x+3)113x)=0


We calculate terms in parentheses: -((-1x+3)113x), so:

(-1x+3)113x

We multiply parentheses

-113x^2+339x

Back to the equation:

-(-113x^2+339x)


We get rid of parentheses

113x^2-339x+x=0

We add all the numbers together, and all the variables

113x^2-338x=0

a = 113; b = -338; c = 0;
Δ = b2-4ac
Δ = -3382-4·113·0
Δ = 114244
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{114244}=338$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-338)-338}{2*113}=\frac{0}{226}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-338)+338}{2*113}=\frac{676}{226}
=2+112/113
$