X/3x-1/4=2+x

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

X/3X-1/4=2+X

We move all terms to the left:

X/3X-1/4-(2+X)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R


We add all the numbers together, and all the variables

X/3X-(X+2)-1/4=0

We get rid of parentheses

X/3X-X-2-1/4=0

We calculate fractions


-X+4X/12X+(-3X)/12X-2=0

We add all the numbers together, and all the variables

-1X+4X/12X+(-3X)/12X-2=0

We multiply all the terms by the denominator


-1X*12X+4X+(-3X)-2*12X=0

We add all the numbers together, and all the variables

4X-1X*12X+(-3X)-2*12X=0

Wy multiply elements

-12X^2+4X+(-3X)-24X=0

We get rid of parentheses

-12X^2+4X-3X-24X=0

We add all the numbers together, and all the variables

-12X^2-23X=0

a = -12; b = -23; c = 0;
Δ = b2-4ac
Δ = -232-4·(-12)·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-23}{2*-12}=\frac{0}{-24}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+23}{2*-12}=\frac{46}{-24}
=-1+11/12
$