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

Solution for 1/3x+1/4=6/6x-1 equation:

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

We move all terms to the left:

1/3x+1/4-(6/6x-1)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 6x-1)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


108x^2/288x^2+96x/288x^2+(-288x)/288x^2+1=0

We multiply all the terms by the denominator


108x^2+96x+(-288x)+1*288x^2=0

Wy multiply elements

108x^2+288x^2+96x+(-288x)=0

We get rid of parentheses

108x^2+288x^2+96x-288x=0

We add all the numbers together, and all the variables

396x^2-192x=0

a = 396; b = -192; c = 0;
Δ = b2-4ac
Δ = -1922-4·396·0
Δ = 36864
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36864}=192$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-192)-192}{2*396}=\frac{0}{792}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-192)+192}{2*396}=\frac{384}{792}
=16/33
$