2/3(27x+15)-1=-1/4(16x-20)

Solution for 2/3(27x+15)-1=-1/4(16x-20) equation:

2/3(27x+15)-1=-1/4(16x-20)

We move all terms to the left:

2/3(27x+15)-1-(-1/4(16x-20))=0


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

x∈R



Domain of the equation: 4(16x-20))!=0

x∈R


We calculate fractions


(8x1/(3(27x+15)*4(16x-20)))+(-(-3x2)/(3(27x+15)*4(16x-20)))-1=0


We calculate terms in parentheses: +(8x1/(3(27x+15)*4(16x-20))), so:

8x1/(3(27x+15)*4(16x-20))

We multiply all the terms by the denominator


8x1

We add all the numbers together, and all the variables

8x

Back to the equation:

+(8x)



We calculate terms in parentheses: +(-(-3x2)/(3(27x+15)*4(16x-20))), so:

-(-3x2)/(3(27x+15)*4(16x-20))

We add all the numbers together, and all the variables

-(-3x^2)/(3(27x+15)*4(16x-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+8x-1=0

a = 3; b = 8; c = -1;
Δ = b2-4ac
Δ = 82-4·3·(-1)
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{19}}{2*3}=\frac{-8-2\sqrt{19}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{19}}{2*3}=\frac{-8+2\sqrt{19}}{6}
$