5/6x-12=-3/2x

Solution for 5/6x-12=-3/2x equation:

5/6x-12=-3/2x

We move all terms to the left:

5/6x-12-(-3/2x)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We get rid of parentheses

5/6x+3/2x-12=0

We calculate fractions


10x/12x^2+18x/12x^2-12=0

We multiply all the terms by the denominator


10x+18x-12*12x^2=0

We add all the numbers together, and all the variables

28x-12*12x^2=0

Wy multiply elements

-144x^2+28x=0

a = -144; b = 28; c = 0;
Δ = b2-4ac
Δ = 282-4·(-144)·0
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-28}{2*-144}=\frac{-56}{-288}
=7/36
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+28}{2*-144}=\frac{0}{-288}
=0
$