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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-336x^2)/144x^2+96x/144x^2+36x/144x^2=0

We multiply all the terms by the denominator


(-336x^2)+96x+36x=0

We add all the numbers together, and all the variables

(-336x^2)+132x=0

We get rid of parentheses

-336x^2+132x=0

a = -336; b = 132; c = 0;
Δ = b2-4ac
Δ = 1322-4·(-336)·0
Δ = 17424
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{17424}=132$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(132)-132}{2*-336}=\frac{-264}{-672}
=11/28
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(132)+132}{2*-336}=\frac{0}{-672}
=0
$