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

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

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

We move all terms to the left:

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


Domain of the equation: 3x-4)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


-12x*3x+4*3x+3*3x-2=0

Wy multiply elements

-36x^2+12x+9x-2=0

We add all the numbers together, and all the variables

-36x^2+21x-2=0

a = -36; b = 21; c = -2;
Δ = b2-4ac
Δ = 212-4·(-36)·(-2)
Δ = 153
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-3\sqrt{17}}{2*-36}=\frac{-21-3\sqrt{17}}{-72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+3\sqrt{17}}{2*-36}=\frac{-21+3\sqrt{17}}{-72}
$