2/3(21x+21)-17=-1/2(18x-8)

Solution for 2/3(21x+21)-17=-1/2(18x-8) equation:

2/3(21x+21)-17=-1/2(18x-8)

We move all terms to the left:

2/3(21x+21)-17-(-1/2(18x-8))=0


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

x∈R



Domain of the equation: 2(18x-8))!=0

x∈R


We calculate fractions


(4x1/(3(21x+21)*2(18x-8)))+(-(-3x2)/(3(21x+21)*2(18x-8)))-17=0


We calculate terms in parentheses: +(4x1/(3(21x+21)*2(18x-8))), so:

4x1/(3(21x+21)*2(18x-8))

We multiply all the terms by the denominator


4x1

We add all the numbers together, and all the variables

4x

Back to the equation:

+(4x)



We calculate terms in parentheses: +(-(-3x2)/(3(21x+21)*2(18x-8))), so:

-(-3x2)/(3(21x+21)*2(18x-8))

We add all the numbers together, and all the variables

-(-3x^2)/(3(21x+21)*2(18x-8))

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+4x-17=0

a = 3; b = 4; c = -17;
Δ = b2-4ac
Δ = 42-4·3·(-17)
Δ = 220
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:

$\sqrt{\Delta}=\sqrt{220}=\sqrt{4*55}=\sqrt{4}*\sqrt{55}=2\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{55}}{2*3}=\frac{-4-2\sqrt{55}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{55}}{2*3}=\frac{-4+2\sqrt{55}}{6}
$