3.33x-(1-x)=5.5x(1-x)-x

Solution for 3.33x-(1-x)=5.5x(1-x)-x equation:

3.33x-(1-x)=5.5x(1-x)-x

We move all terms to the left:

3.33x-(1-x)-(5.5x(1-x)-x)=0

We add all the numbers together, and all the variables

3.33x-(-1x+1)-(5.5x(-1x+1)-x)=0

We get rid of parentheses

3.33x+1x-(5.5x(-1x+1)-x)-1=0


We calculate terms in parentheses: -(5.5x(-1x+1)-x), so:

5.5x(-1x+1)-x

We add all the numbers together, and all the variables

-1x+5.5x(-1x+1)

We multiply parentheses

-5x^2-1x+5x

We add all the numbers together, and all the variables

-5x^2+4x

Back to the equation:

-(-5x^2+4x)


We add all the numbers together, and all the variables

-(-5x^2+4x)+4.33x-1=0

We get rid of parentheses

5x^2-4x+4.33x-1=0

We add all the numbers together, and all the variables

5x^2+0.33x-1=0

a = 5; b = 0.33; c = -1;
Δ = b2-4ac
Δ = 0.332-4·5·(-1)
Δ = 20.1089
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{-(0.33)-\sqrt{20.1089}}{2*5}=\frac{-0.33-\sqrt{20.1089}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.33)+\sqrt{20.1089}}{2*5}=\frac{-0.33+\sqrt{20.1089}}{10}
$