-5/3x+12=3/2x-7

Solution for -5/3x+12=3/2x-7 equation:

-5/3x+12=3/2x-7

We move all terms to the left:

-5/3x+12-(3/2x-7)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x-7)!=0

x∈R


We get rid of parentheses

-5/3x-3/2x+7+12=0

We calculate fractions


(-10x)/6x^2+(-9x)/6x^2+7+12=0

We add all the numbers together, and all the variables

(-10x)/6x^2+(-9x)/6x^2+19=0

We multiply all the terms by the denominator


(-10x)+(-9x)+19*6x^2=0

Wy multiply elements

114x^2+(-10x)+(-9x)=0

We get rid of parentheses

114x^2-10x-9x=0

We add all the numbers together, and all the variables

114x^2-19x=0

a = 114; b = -19; c = 0;
Δ = b2-4ac
Δ = -192-4·114·0
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-19}{2*114}=\frac{0}{228}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+19}{2*114}=\frac{38}{228}
=1/6
$