3/4(24x+24)-18=-1/2(14x-6)

Solution for 3/4(24x+24)-18=-1/2(14x-6) equation:

3/4(24x+24)-18=-1/2(14x-6)

We move all terms to the left:

3/4(24x+24)-18-(-1/2(14x-6))=0


Domain of the equation: 4(24x+24)!=0

x∈R



Domain of the equation: 2(14x-6))!=0

x∈R


We calculate fractions


(6x1/(4(24x+24)*2(14x-6)))+(-(-4x2)/(4(24x+24)*2(14x-6)))-18=0


We calculate terms in parentheses: +(6x1/(4(24x+24)*2(14x-6))), so:

6x1/(4(24x+24)*2(14x-6))

We multiply all the terms by the denominator


6x1

We add all the numbers together, and all the variables

6x

Back to the equation:

+(6x)



We calculate terms in parentheses: +(-(-4x2)/(4(24x+24)*2(14x-6))), so:

-(-4x2)/(4(24x+24)*2(14x-6))

We add all the numbers together, and all the variables

-(-4x^2)/(4(24x+24)*2(14x-6))

We multiply all the terms by the denominator


-(-4x^2)

We get rid of parentheses

4x^2

Back to the equation:

+(4x^2)


determiningTheFunctionDomain
4x^2+6x-18=0

a = 4; b = 6; c = -18;
Δ = b2-4ac
Δ = 62-4·4·(-18)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-18}{2*4}=\frac{-24}{8}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+18}{2*4}=\frac{12}{8}
=1+1/2
$