34-6/1x=13+6/5x

Solution for 34-6/1x=13+6/5x equation:

34-6/1x=13+6/5x

We move all terms to the left:

34-6/1x-(13+6/5x)=0


Domain of the equation: 1x!=0

x∈R



Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-6/1x-(6/5x+13)+34=0

We get rid of parentheses

-6/1x-6/5x-13+34=0

We calculate fractions


(-30x)/5x^2+(-6x)/5x^2-13+34=0

We add all the numbers together, and all the variables

(-30x)/5x^2+(-6x)/5x^2+21=0

We multiply all the terms by the denominator


(-30x)+(-6x)+21*5x^2=0

Wy multiply elements

105x^2+(-30x)+(-6x)=0

We get rid of parentheses

105x^2-30x-6x=0

We add all the numbers together, and all the variables

105x^2-36x=0

a = 105; b = -36; c = 0;
Δ = b2-4ac
Δ = -362-4·105·0
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-36}{2*105}=\frac{0}{210}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+36}{2*105}=\frac{72}{210}
=12/35
$