1/3(21x+15)-16=-1/2(16x-12)

Solution for 1/3(21x+15)-16=-1/2(16x-12) equation:

1/3(21x+15)-16=-1/2(16x-12)

We move all terms to the left:

1/3(21x+15)-16-(-1/2(16x-12))=0


Domain of the equation: 3(21x+15)!=0

x∈R



Domain of the equation: 2(16x-12))!=0

x∈R


We calculate fractions


(2x1/(3(21x+15)*2(16x-12)))+(-(-3x2)/(3(21x+15)*2(16x-12)))-16=0


We calculate terms in parentheses: +(2x1/(3(21x+15)*2(16x-12))), so:

2x1/(3(21x+15)*2(16x-12))

We multiply all the terms by the denominator


2x1

We add all the numbers together, and all the variables

2x

Back to the equation:

+(2x)



We calculate terms in parentheses: +(-(-3x2)/(3(21x+15)*2(16x-12))), so:

-(-3x2)/(3(21x+15)*2(16x-12))

We add all the numbers together, and all the variables

-(-3x^2)/(3(21x+15)*2(16x-12))

We multiply all the terms by the denominator


-(-3x^2)

We get rid of parentheses

3x^2

Back to the equation:

+(3x^2)


determiningTheFunctionDomain
3x^2+2x-16=0

a = 3; b = 2; c = -16;
Δ = b2-4ac
Δ = 22-4·3·(-16)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-14}{2*3}=\frac{-16}{6}
=-2+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+14}{2*3}=\frac{12}{6}
=2
$