(-2/3x-7)-(-12+1/6x)=

Solution for (-2/3x-7)-(-12+1/6x)= equation:

(-2/3x-7)-(-12+1/6x)=

We move all terms to the left:

(-2/3x-7)-(-12+1/6x)-()=0


Domain of the equation: 3x-7)!=0

x∈R



Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(-2/3x-7)-(1/6x-12)-()=0

We add all the numbers together, and all the variables

(-2/3x-7)-(1/6x-12)=0

We get rid of parentheses

-2/3x-1/6x-7+12=0

We calculate fractions


(-12x)/18x^2+(-3x)/18x^2-7+12=0

We add all the numbers together, and all the variables

(-12x)/18x^2+(-3x)/18x^2+5=0

We multiply all the terms by the denominator


(-12x)+(-3x)+5*18x^2=0

Wy multiply elements

90x^2+(-12x)+(-3x)=0

We get rid of parentheses

90x^2-12x-3x=0

We add all the numbers together, and all the variables

90x^2-15x=0

a = 90; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·90·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-15}{2*90}=\frac{0}{180}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*90}=\frac{30}{180}
=1/6
$