1/2x+.3333333=3x-3

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Solution for 1/2x+.3333333=3x-3 equation: 



1/2x+.3333333=3x-3

We move all terms to the left:

1/2x+.3333333-(3x-3)=0



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



We add all the numbers together, and all the variables

1/2x-(3x-3)+0.3333333=0

We get rid of parentheses

1/2x-3x+3+0.3333333=0

We multiply all the terms by the denominator


-3x*2x+3*2x+(0.3333333)*2x+1=0

We multiply parentheses

-3x*2x+3*2x+0.6666666x+1=0

Wy multiply elements

-6x^2+6x+0.6666666x+1=0

We add all the numbers together, and all the variables

-6x^2+6.6666666x+1=0

a = -6; b = 6.6666666; c = +1;
Δ = b2-4ac
Δ = 6.66666662-4·(-6)·1
Δ = 68.444443555556
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{-(6.6666666)-\sqrt{68.444443555556}}{2*-6}=\frac{-6.6666666-\sqrt{68.444443555556}}{-12}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6.6666666)+\sqrt{68.444443555556}}{2*-6}=\frac{-6.6666666+\sqrt{68.444443555556}}{-12}
$

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