1/5x+6=3/1x+5

Solution for 1/5x+6=3/1x+5 equation:

1/5x+6=3/1x+5

We move all terms to the left:

1/5x+6-(3/1x+5)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



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

x∈R


We get rid of parentheses

1/5x-3/1x-5+6=0

We calculate fractions


x/5x^2+(-15x)/5x^2-5+6=0

We add all the numbers together, and all the variables

x/5x^2+(-15x)/5x^2+1=0

We multiply all the terms by the denominator


x+(-15x)+1*5x^2=0

Wy multiply elements

5x^2+x+(-15x)=0

We get rid of parentheses

5x^2+x-15x=0

We add all the numbers together, and all the variables

5x^2-14x=0

a = 5; b = -14; c = 0;
Δ = b2-4ac
Δ = -142-4·5·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-14}{2*5}=\frac{0}{10}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14}{2*5}=\frac{28}{10}
=2+4/5
$