(0.333+x)/(0.333-x)(0.333+x)=5

Solution for (0.333+x)/(0.333-x)(0.333+x)=5 equation:

(0.333+x)/(0.333-x)(0.333+x)=5

We move all terms to the left:

(0.333+x)/(0.333-x)(0.333+x)-(5)=0


Domain of the equation: (0.333-x)(0.333+x)!=0

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

-x)(0.333+x!=-0.333

x∈R


We add all the numbers together, and all the variables

(x+0.333)/(-1x+0.333)(x+0.333)-5=0

We multiply parentheses ..

(x+0.333)/(-1x^2-0.333x+0.333x+0.110889)-5=0

We multiply all the terms by the denominator


-5*(-1x^2-0.333x+0.333x+0.110889)+(x+0.333)=0

We multiply parentheses

5x^2-0x-0x+(x+0.333)-0.554445=0

We get rid of parentheses

5x^2-0x-0x+x+0.333-0.554445=0

We add all the numbers together, and all the variables

5x^2-1x-0.221445=0

a = 5; b = -1; c = -0.221445;
Δ = b2-4ac
Δ = -12-4·5·(-0.221445)
Δ = 5.4289
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{-(-1)-\sqrt{5.4289}}{2*5}=\frac{1-\sqrt{5.4289}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{5.4289}}{2*5}=\frac{1+\sqrt{5.4289}}{10}
$