1/3x+1/4=1/2x+6

Solution for 1/3x+1/4=1/2x+6 equation:

1/3x+1/4=1/2x+6

We move all terms to the left:

1/3x+1/4-(1/2x+6)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x+6)!=0

x∈R


We get rid of parentheses

1/3x-1/2x-6+1/4=0

We calculate fractions


12x^2/96x^2+32x/96x^2+(-48x)/96x^2-6=0

We multiply all the terms by the denominator


12x^2+32x+(-48x)-6*96x^2=0

Wy multiply elements

12x^2-576x^2+32x+(-48x)=0

We get rid of parentheses

12x^2-576x^2+32x-48x=0

We add all the numbers together, and all the variables

-564x^2-16x=0

a = -564; b = -16; c = 0;
Δ = b2-4ac
Δ = -162-4·(-564)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-16}{2*-564}=\frac{0}{-1128}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16}{2*-564}=\frac{32}{-1128}
=-4/141
$