3/4(20x+32)-1=-2/3(15x-9)

Solution for 3/4(20x+32)-1=-2/3(15x-9) equation:

3/4(20x+32)-1=-2/3(15x-9)

We move all terms to the left:

3/4(20x+32)-1-(-2/3(15x-9))=0


Domain of the equation: 4(20x+32)!=0

x∈R



Domain of the equation: 3(15x-9))!=0

x∈R


We calculate fractions


(9x1/(4(20x+32)*3(15x-9)))+(-(-8x2)/(4(20x+32)*3(15x-9)))-1=0


We calculate terms in parentheses: +(9x1/(4(20x+32)*3(15x-9))), so:

9x1/(4(20x+32)*3(15x-9))

We multiply all the terms by the denominator


9x1

We add all the numbers together, and all the variables

9x

Back to the equation:

+(9x)



We calculate terms in parentheses: +(-(-8x2)/(4(20x+32)*3(15x-9))), so:

-(-8x2)/(4(20x+32)*3(15x-9))

We add all the numbers together, and all the variables

-(-8x^2)/(4(20x+32)*3(15x-9))

We multiply all the terms by the denominator


-(-8x^2)

We get rid of parentheses

8x^2

Back to the equation:

+(8x^2)


determiningTheFunctionDomain
8x^2+9x-1=0

a = 8; b = 9; c = -1;
Δ = b2-4ac
Δ = 92-4·8·(-1)
Δ = 113
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{-(9)-\sqrt{113}}{2*8}=\frac{-9-\sqrt{113}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{113}}{2*8}=\frac{-9+\sqrt{113}}{16}
$