2/3x+7/12x=1/4

Solution for 2/3x+7/12x=1/4 equation:

2/3x+7/12x=1/4

We move all terms to the left:

2/3x+7/12x-(1/4)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 12x!=0

x!=0/12

x!=0

x∈R


We add all the numbers together, and all the variables

2/3x+7/12x-(+1/4)=0

We get rid of parentheses

2/3x+7/12x-1/4=0

We calculate fractions


(-36x^2)/576x^2+384x/576x^2+336x/576x^2=0

We multiply all the terms by the denominator


(-36x^2)+384x+336x=0

We add all the numbers together, and all the variables

(-36x^2)+720x=0

We get rid of parentheses

-36x^2+720x=0

a = -36; b = 720; c = 0;
Δ = b2-4ac
Δ = 7202-4·(-36)·0
Δ = 518400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{518400}=720$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(720)-720}{2*-36}=\frac{-1440}{-72}
=+20
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(720)+720}{2*-36}=\frac{0}{-72}
=0
$