1/4(20x+32)-17=-1/2(18x-6)

Solution for 1/4(20x+32)-17=-1/2(18x-6) equation:

1/4(20x+32)-17=-1/2(18x-6)

We move all terms to the left:

1/4(20x+32)-17-(-1/2(18x-6))=0


Domain of the equation: 4(20x+32)!=0

x∈R



Domain of the equation: 2(18x-6))!=0

x∈R


We calculate fractions


(2x1/(4(20x+32)*2(18x-6)))+(-(-4x2)/(4(20x+32)*2(18x-6)))-17=0


We calculate terms in parentheses: +(2x1/(4(20x+32)*2(18x-6))), so:

2x1/(4(20x+32)*2(18x-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(20x+32)*2(18x-6))), so:

-(-4x2)/(4(20x+32)*2(18x-6))

We add all the numbers together, and all the variables

-(-4x^2)/(4(20x+32)*2(18x-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-17=0

a = 4; b = 2; c = -17;
Δ = b2-4ac
Δ = 22-4·4·(-17)
Δ = 276
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:

$\sqrt{\Delta}=\sqrt{276}=\sqrt{4*69}=\sqrt{4}*\sqrt{69}=2\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{69}}{2*4}=\frac{-2-2\sqrt{69}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{69}}{2*4}=\frac{-2+2\sqrt{69}}{8}
$