1/3(27x+15)-8=-1/5(10x-20)

Solution for 1/3(27x+15)-8=-1/5(10x-20) equation:

1/3(27x+15)-8=-1/5(10x-20)

We move all terms to the left:

1/3(27x+15)-8-(-1/5(10x-20))=0


Domain of the equation: 3(27x+15)!=0

x∈R



Domain of the equation: 5(10x-20))!=0

x∈R


We calculate fractions


(5x1/(3(27x+15)*5(10x-20)))+(-(-3x2)/(3(27x+15)*5(10x-20)))-8=0


We calculate terms in parentheses: +(5x1/(3(27x+15)*5(10x-20))), so:

5x1/(3(27x+15)*5(10x-20))

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(27x+15)*5(10x-20))), so:

-(-3x2)/(3(27x+15)*5(10x-20))

We add all the numbers together, and all the variables

-(-3x^2)/(3(27x+15)*5(10x-20))

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-8=0

a = 3; b = 5; c = -8;
Δ = b2-4ac
Δ = 52-4·3·(-8)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-11}{2*3}=\frac{-16}{6}
=-2+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+11}{2*3}=\frac{6}{6}
=1
$