1/2(18x+8)-2=-3/4(24x-32)

Solution for 1/2(18x+8)-2=-3/4(24x-32) equation:

1/2(18x+8)-2=-3/4(24x-32)

We move all terms to the left:

1/2(18x+8)-2-(-3/4(24x-32))=0


Domain of the equation: 2(18x+8)!=0

x∈R



Domain of the equation: 4(24x-32))!=0

x∈R


We calculate fractions


(4x2/(2(18x+8)*4(24x-32)))+(-(-6x1)/(2(18x+8)*4(24x-32)))-2=0


We calculate terms in parentheses: +(4x2/(2(18x+8)*4(24x-32))), so:

4x2/(2(18x+8)*4(24x-32))

We multiply all the terms by the denominator


4x2

We add all the numbers together, and all the variables

4x^2

Back to the equation:

+(4x^2)



We calculate terms in parentheses: +(-(-6x1)/(2(18x+8)*4(24x-32))), so:

-(-6x1)/(2(18x+8)*4(24x-32))

We add all the numbers together, and all the variables

-(-6x)/(2(18x+8)*4(24x-32))

We multiply all the terms by the denominator


-(-6x)

We get rid of parentheses

6x

Back to the equation:

+(6x)


a = 4; b = 6; c = -2;
Δ = b2-4ac
Δ = 62-4·4·(-2)
Δ = 68
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:

$\sqrt{\Delta}=\sqrt{68}=\sqrt{4*17}=\sqrt{4}*\sqrt{17}=2\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{17}}{2*4}=\frac{-6-2\sqrt{17}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{17}}{2*4}=\frac{-6+2\sqrt{17}}{8}
$