1/314x-6=3/48x+12

Solution for 1/314x-6=3/48x+12 equation:

1/314x-6=3/48x+12

We move all terms to the left:

1/314x-6-(3/48x+12)=0


Domain of the equation: 314x!=0

x!=0/314

x!=0

x∈R



Domain of the equation: 48x+12)!=0

x∈R


We get rid of parentheses

1/314x-3/48x-12-6=0

We calculate fractions


48x/15072x^2+(-942x)/15072x^2-12-6=0

We add all the numbers together, and all the variables

48x/15072x^2+(-942x)/15072x^2-18=0

We multiply all the terms by the denominator


48x+(-942x)-18*15072x^2=0

Wy multiply elements

-271296x^2+48x+(-942x)=0

We get rid of parentheses

-271296x^2+48x-942x=0

We add all the numbers together, and all the variables

-271296x^2-894x=0

a = -271296; b = -894; c = 0;
Δ = b2-4ac
Δ = -8942-4·(-271296)·0
Δ = 799236
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{799236}=894$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-894)-894}{2*-271296}=\frac{0}{-542592}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-894)+894}{2*-271296}=\frac{1788}{-542592}
=-149/45216
$