3-4x=-6(2/3x-12)

Solution for 3-4x=-6(2/3x-12) equation:

3-4x=-6(2/3x-12)

We move all terms to the left:

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


Domain of the equation: 3x-12))!=0

x∈R


We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

-4x*3x+3*3x-12))-(-6(-10))=0

We add all the numbers together, and all the variables

-4x*3x+3*3x=0

Wy multiply elements

-12x^2+9x=0

a = -12; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-12)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*-12}=\frac{-18}{-24}
=3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-12}=\frac{0}{-24}
=0
$