1/3(21x+9)-6=-1/5(10x-10)

Solution for 1/3(21x+9)-6=-1/5(10x-10) equation:

1/3(21x+9)-6=-1/5(10x-10)

We move all terms to the left:

1/3(21x+9)-6-(-1/5(10x-10))=0


Domain of the equation: 3(21x+9)!=0

x∈R



Domain of the equation: 5(10x-10))!=0

x∈R


We calculate fractions


(5x1/(3(21x+9)*5(10x-10)))+(-(-3x2)/(3(21x+9)*5(10x-10)))-6=0


We calculate terms in parentheses: +(5x1/(3(21x+9)*5(10x-10))), so:

5x1/(3(21x+9)*5(10x-10))

We multiply all the terms by the denominator


5x1

We add all the numbers together, and all the variables

5x

Back to the equation:

+(5x)



We calculate terms in parentheses: +(-(-3x2)/(3(21x+9)*5(10x-10))), so:

-(-3x2)/(3(21x+9)*5(10x-10))

We add all the numbers together, and all the variables

-(-3x^2)/(3(21x+9)*5(10x-10))

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+5x-6=0

a = 3; b = 5; c = -6;
Δ = b2-4ac
Δ = 52-4·3·(-6)
Δ = 97
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{97}}{2*3}=\frac{-5-\sqrt{97}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{97}}{2*3}=\frac{-5+\sqrt{97}}{6}
$