1/2x+5=5/5x+1

Solution for 1/2x+5=5/5x+1 equation:

1/2x+5=5/5x+1

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 5x+1)!=0

x∈R


We get rid of parentheses

1/2x-5/5x-1+5=0

We calculate fractions


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

We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


5x+(-10x)+4*10x^2=0

Wy multiply elements

40x^2+5x+(-10x)=0

We get rid of parentheses

40x^2+5x-10x=0

We add all the numbers together, and all the variables

40x^2-5x=0

a = 40; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·40·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*40}=\frac{0}{80}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*40}=\frac{10}{80}
=1/8
$