1/6x+2/3x=3/8+1

Solution for 1/6x+2/3x=3/8+1 equation:

1/6x+2/3x=3/8+1

We move all terms to the left:

1/6x+2/3x-(3/8+1)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

1/6x+2/3x-1-3/8=0

We calculate fractions


(-162x^2)/1152x^2+192x/1152x^2+768x/1152x^2-1=0

We multiply all the terms by the denominator


(-162x^2)+192x+768x-1*1152x^2=0

We add all the numbers together, and all the variables

(-162x^2)+960x-1*1152x^2=0

Wy multiply elements

(-162x^2)-1152x^2+960x=0

We get rid of parentheses

-162x^2-1152x^2+960x=0

We add all the numbers together, and all the variables

-1314x^2+960x=0

a = -1314; b = 960; c = 0;
Δ = b2-4ac
Δ = 9602-4·(-1314)·0
Δ = 921600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{921600}=960$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(960)-960}{2*-1314}=\frac{-1920}{-2628}
=160/219
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(960)+960}{2*-1314}=\frac{0}{-2628}
=0
$