2/3x-7=3x+12

Solution for 2/3x-7=3x+12 equation:

2/3x-7=3x+12

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

2/3x-3x-12-7=0

We multiply all the terms by the denominator


-3x*3x-12*3x-7*3x+2=0

Wy multiply elements

-9x^2-36x-21x+2=0

We add all the numbers together, and all the variables

-9x^2-57x+2=0

a = -9; b = -57; c = +2;
Δ = b2-4ac
Δ = -572-4·(-9)·2
Δ = 3321
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:

$\sqrt{\Delta}=\sqrt{3321}=\sqrt{81*41}=\sqrt{81}*\sqrt{41}=9\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-57)-9\sqrt{41}}{2*-9}=\frac{57-9\sqrt{41}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-57)+9\sqrt{41}}{2*-9}=\frac{57+9\sqrt{41}}{-18}
$