6/x+4=112/5x-13

Solution for 6/x+4=112/5x-13 equation:

6/x+4=112/5x-13

We move all terms to the left:

6/x+4-(112/5x-13)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 5x-13)!=0

x∈R


We get rid of parentheses

6/x-112/5x+13+4=0

We calculate fractions


30x/5x^2+(-112x)/5x^2+13+4=0

We add all the numbers together, and all the variables

30x/5x^2+(-112x)/5x^2+17=0

We multiply all the terms by the denominator


30x+(-112x)+17*5x^2=0

Wy multiply elements

85x^2+30x+(-112x)=0

We get rid of parentheses

85x^2+30x-112x=0

We add all the numbers together, and all the variables

85x^2-82x=0

a = 85; b = -82; c = 0;
Δ = b2-4ac
Δ = -822-4·85·0
Δ = 6724
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6724}=82$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-82)-82}{2*85}=\frac{0}{170}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-82)+82}{2*85}=\frac{164}{170}
=82/85
$