7/6x+4=3/12x-2

Solution for 7/6x+4=3/12x-2 equation:

7/6x+4=3/12x-2

We move all terms to the left:

7/6x+4-(3/12x-2)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 12x-2)!=0

x∈R


We get rid of parentheses

7/6x-3/12x+2+4=0

We calculate fractions


84x/72x^2+(-18x)/72x^2+2+4=0

We add all the numbers together, and all the variables

84x/72x^2+(-18x)/72x^2+6=0

We multiply all the terms by the denominator


84x+(-18x)+6*72x^2=0

Wy multiply elements

432x^2+84x+(-18x)=0

We get rid of parentheses

432x^2+84x-18x=0

We add all the numbers together, and all the variables

432x^2+66x=0

a = 432; b = 66; c = 0;
Δ = b2-4ac
Δ = 662-4·432·0
Δ = 4356
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4356}=66$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(66)-66}{2*432}=\frac{-132}{864}
=-11/72
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(66)+66}{2*432}=\frac{0}{864}
=0
$