1/3x+9-1/6x=13

Solution for 1/3x+9-1/6x=13 equation:

1/3x+9-1/6x=13

We move all terms to the left:

1/3x+9-1/6x-(13)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We add all the numbers together, and all the variables

1/3x-1/6x-4=0

We calculate fractions


6x/18x^2+(-3x)/18x^2-4=0

We multiply all the terms by the denominator


6x+(-3x)-4*18x^2=0

Wy multiply elements

-72x^2+6x+(-3x)=0

We get rid of parentheses

-72x^2+6x-3x=0

We add all the numbers together, and all the variables

-72x^2+3x=0

a = -72; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-72)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*-72}=\frac{-6}{-144}
=1/24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-72}=\frac{0}{-144}
=0
$