3/4(24x+20)-8=-1/2(12x-18)

Solution for 3/4(24x+20)-8=-1/2(12x-18) equation:

3/4(24x+20)-8=-1/2(12x-18)

We move all terms to the left:

3/4(24x+20)-8-(-1/2(12x-18))=0


Domain of the equation: 4(24x+20)!=0

x∈R



Domain of the equation: 2(12x-18))!=0

x∈R


We calculate fractions


(6x1/(4(24x+20)*2(12x-18)))+(-(-4x2)/(4(24x+20)*2(12x-18)))-8=0


We calculate terms in parentheses: +(6x1/(4(24x+20)*2(12x-18))), so:

6x1/(4(24x+20)*2(12x-18))

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+20)*2(12x-18))), so:

-(-4x2)/(4(24x+20)*2(12x-18))

We add all the numbers together, and all the variables

-(-4x^2)/(4(24x+20)*2(12x-18))

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-8=0

a = 4; b = 6; c = -8;
Δ = b2-4ac
Δ = 62-4·4·(-8)
Δ = 164
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:

$\sqrt{\Delta}=\sqrt{164}=\sqrt{4*41}=\sqrt{4}*\sqrt{41}=2\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{41}}{2*4}=\frac{-6-2\sqrt{41}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{41}}{2*4}=\frac{-6+2\sqrt{41}}{8}
$