1/28x+5=17+1/7x

Solution for 1/28x+5=17+1/7x equation:

1/28x+5=17+1/7x

We move all terms to the left:

1/28x+5-(17+1/7x)=0


Domain of the equation: 28x!=0

x!=0/28

x!=0

x∈R



Domain of the equation: 7x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/28x-(1/7x+17)+5=0

We get rid of parentheses

1/28x-1/7x-17+5=0

We calculate fractions


7x/196x^2+(-28x)/196x^2-17+5=0

We add all the numbers together, and all the variables

7x/196x^2+(-28x)/196x^2-12=0

We multiply all the terms by the denominator


7x+(-28x)-12*196x^2=0

Wy multiply elements

-2352x^2+7x+(-28x)=0

We get rid of parentheses

-2352x^2+7x-28x=0

We add all the numbers together, and all the variables

-2352x^2-21x=0

a = -2352; b = -21; c = 0;
Δ = b2-4ac
Δ = -212-4·(-2352)·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-21}{2*-2352}=\frac{0}{-4704}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+21}{2*-2352}=\frac{42}{-4704}
=-1/112
$