1/5(2x-10)=-1/4(-4x+1)

Solution for 1/5(2x-10)=-1/4(-4x+1) equation:

1/5(2x-10)=-1/4(-4x+1)

We move all terms to the left:

1/5(2x-10)-(-1/4(-4x+1))=0


Domain of the equation: 5(2x-10)!=0

x∈R



Domain of the equation: 4(-4x+1))!=0

x∈R


We calculate fractions


(4x(-)/(5(2x-10)*4(-4x+1)))+(-(-5x2)/(5(2x-10)*4(-4x+1)))=0


We calculate terms in parentheses: +(4x(-)/(5(2x-10)*4(-4x+1))), so:

4x(-)/(5(2x-10)*4(-4x+1))

We add all the numbers together, and all the variables

4x0/(5(2x-10)*4(-4x+1))

We multiply all the terms by the denominator


4x0

We add all the numbers together, and all the variables

4x

Back to the equation:

+(4x)



We calculate terms in parentheses: +(-(-5x2)/(5(2x-10)*4(-4x+1))), so:

-(-5x2)/(5(2x-10)*4(-4x+1))

We add all the numbers together, and all the variables

-(-5x^2)/(5(2x-10)*4(-4x+1))

We multiply all the terms by the denominator


-(-5x^2)

We get rid of parentheses

5x^2

Back to the equation:

+(5x^2)


determiningTheFunctionDomain
5x^2+4x=0

a = 5; b = 4; c = 0;
Δ = b2-4ac
Δ = 42-4·5·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4}{2*5}=\frac{-8}{10}
=-4/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4}{2*5}=\frac{0}{10}
=0
$