1/3x+1/2x=1/2+12

Solution for 1/3x+1/2x=1/2+12 equation:

1/3x+1/2x=1/2+12

We move all terms to the left:

1/3x+1/2x-(1/2+12)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

1/3x+1/2x-12-1/2=0

We calculate fractions


8x/24x^2+3x/24x^2+(-3x)/24x^2-12=0

We multiply all the terms by the denominator


8x+3x+(-3x)-12*24x^2=0

We add all the numbers together, and all the variables

11x+(-3x)-12*24x^2=0

Wy multiply elements

-288x^2+11x+(-3x)=0

We get rid of parentheses

-288x^2+11x-3x=0

We add all the numbers together, and all the variables

-288x^2+8x=0

a = -288; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·(-288)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*-288}=\frac{-16}{-576}
=1/36
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*-288}=\frac{0}{-576}
=0
$