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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 4x+3)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


336x^2/144x^2+336x/144x^2+(-36x)/144x^2-3=0

We multiply all the terms by the denominator


336x^2+336x+(-36x)-3*144x^2=0

Wy multiply elements

336x^2-432x^2+336x+(-36x)=0

We get rid of parentheses

336x^2-432x^2+336x-36x=0

We add all the numbers together, and all the variables

-96x^2+300x=0

a = -96; b = 300; c = 0;
Δ = b2-4ac
Δ = 3002-4·(-96)·0
Δ = 90000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{90000}=300$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(300)-300}{2*-96}=\frac{-600}{-192}
=3+1/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(300)+300}{2*-96}=\frac{0}{-192}
=0
$