1/3x+1/3=12/313x+13=123

Solution for 1/3x+1/3=12/313x+13=123 equation:

1/3x+1/3=12/313x+13=123

We move all terms to the left:

1/3x+1/3-(12/313x+13)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 313x+13)!=0

x∈R


We get rid of parentheses

1/3x-12/313x-13+1/3=0

We calculate fractions


313x/8451x^2+(-324x)/8451x^2+313x/8451x^2-13=0

We multiply all the terms by the denominator


313x+(-324x)+313x-13*8451x^2=0

We add all the numbers together, and all the variables

626x+(-324x)-13*8451x^2=0

Wy multiply elements

-109863x^2+626x+(-324x)=0

We get rid of parentheses

-109863x^2+626x-324x=0

We add all the numbers together, and all the variables

-109863x^2+302x=0

a = -109863; b = 302; c = 0;
Δ = b2-4ac
Δ = 3022-4·(-109863)·0
Δ = 91204
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{91204}=302$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(302)-302}{2*-109863}=\frac{-604}{-219726}
=302/109863
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(302)+302}{2*-109863}=\frac{0}{-219726}
=0
$