1/4(20x+16)=-1/2(10x+32)

Solution for 1/4(20x+16)=-1/2(10x+32) equation:

1/4(20x+16)=-1/2(10x+32)

We move all terms to the left:

1/4(20x+16)-(-1/2(10x+32))=0


Domain of the equation: 4(20x+16)!=0

x∈R



Domain of the equation: 2(10x+32))!=0

x∈R


We calculate fractions


(2x1/(4(20x+16)*2(10x+32)))+(-(-4x2)/(4(20x+16)*2(10x+32)))=0


We calculate terms in parentheses: +(2x1/(4(20x+16)*2(10x+32))), so:

2x1/(4(20x+16)*2(10x+32))

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+16)*2(10x+32))), so:

-(-4x2)/(4(20x+16)*2(10x+32))

We add all the numbers together, and all the variables

-(-4x^2)/(4(20x+16)*2(10x+32))

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=0

a = 4; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·4·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*4}=\frac{-4}{8}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*4}=\frac{0}{8}
=0
$