1/4(28x+8)-4=-1/2(14x-6)

Solution for 1/4(28x+8)-4=-1/2(14x-6) equation:

1/4(28x+8)-4=-1/2(14x-6)

We move all terms to the left:

1/4(28x+8)-4-(-1/2(14x-6))=0


Domain of the equation: 4(28x+8)!=0

x∈R



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

x∈R


We calculate fractions


(2x1/(4(28x+8)*2(14x-6)))+(-(-4x2)/(4(28x+8)*2(14x-6)))-4=0


We calculate terms in parentheses: +(2x1/(4(28x+8)*2(14x-6))), so:

2x1/(4(28x+8)*2(14x-6))

We multiply all the terms by the denominator


2x1

We add all the numbers together, and all the variables

2x

Back to the equation:

+(2x)



We calculate terms in parentheses: +(-(-4x2)/(4(28x+8)*2(14x-6))), so:

-(-4x2)/(4(28x+8)*2(14x-6))

We add all the numbers together, and all the variables

-(-4x^2)/(4(28x+8)*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+2x-4=0

a = 4; b = 2; c = -4;
Δ = b2-4ac
Δ = 22-4·4·(-4)
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{-(2)-2\sqrt{17}}{2*4}=\frac{-2-2\sqrt{17}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{17}}{2*4}=\frac{-2+2\sqrt{17}}{8}
$