5/6x+12=1/4x-2

Solution for 5/6x+12=1/4x-2 equation:

5/6x+12=1/4x-2

We move all terms to the left:

5/6x+12-(1/4x-2)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 4x-2)!=0

x∈R


We get rid of parentheses

5/6x-1/4x+2+12=0

We calculate fractions


20x/24x^2+(-6x)/24x^2+2+12=0

We add all the numbers together, and all the variables

20x/24x^2+(-6x)/24x^2+14=0

We multiply all the terms by the denominator


20x+(-6x)+14*24x^2=0

Wy multiply elements

336x^2+20x+(-6x)=0

We get rid of parentheses

336x^2+20x-6x=0

We add all the numbers together, and all the variables

336x^2+14x=0

a = 336; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·336·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14}{2*336}=\frac{-28}{672}
=-1/24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*336}=\frac{0}{672}
=0
$