1/8x+1/3x+1/8=29/12

Solution for 1/8x+1/3x+1/8=29/12 equation:

1/8x+1/3x+1/8=29/12

We move all terms to the left:

1/8x+1/3x+1/8-(29/12)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

1/8x+1/3x+1/8-(+29/12)=0

We get rid of parentheses

1/8x+1/3x+1/8-29/12=0

We calculate fractions


(-16704x^2)/18432x^2+36x/18432x^2+6144x/18432x^2+36x/18432x^2=0

We multiply all the terms by the denominator


(-16704x^2)+36x+6144x+36x=0

We add all the numbers together, and all the variables

(-16704x^2)+6216x=0

We get rid of parentheses

-16704x^2+6216x=0

a = -16704; b = 6216; c = 0;
Δ = b2-4ac
Δ = 62162-4·(-16704)·0
Δ = 38638656
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{38638656}=6216$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6216)-6216}{2*-16704}=\frac{-12432}{-33408}
=259/696
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6216)+6216}{2*-16704}=\frac{0}{-33408}
=0
$