1/4(28x+28)-19=-2/3(18x-18)

Solution for 1/4(28x+28)-19=-2/3(18x-18) equation:

1/4(28x+28)-19=-2/3(18x-18)

We move all terms to the left:

1/4(28x+28)-19-(-2/3(18x-18))=0


Domain of the equation: 4(28x+28)!=0

x∈R



Domain of the equation: 3(18x-18))!=0

x∈R


We calculate fractions


(3x1/(4(28x+28)*3(18x-18)))+(-(-8x2)/(4(28x+28)*3(18x-18)))-19=0


We calculate terms in parentheses: +(3x1/(4(28x+28)*3(18x-18))), so:

3x1/(4(28x+28)*3(18x-18))

We multiply all the terms by the denominator


3x1

We add all the numbers together, and all the variables

3x

Back to the equation:

+(3x)



We calculate terms in parentheses: +(-(-8x2)/(4(28x+28)*3(18x-18))), so:

-(-8x2)/(4(28x+28)*3(18x-18))

We add all the numbers together, and all the variables

-(-8x^2)/(4(28x+28)*3(18x-18))

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+3x-19=0

a = 8; b = 3; c = -19;
Δ = b2-4ac
Δ = 32-4·8·(-19)
Δ = 617
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{-(3)-\sqrt{617}}{2*8}=\frac{-3-\sqrt{617}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{617}}{2*8}=\frac{-3+\sqrt{617}}{16}
$