5/x=7/6x+1

Solution for 5/x=7/6x+1 equation:

5/x=7/6x+1

We move all terms to the left:

5/x-(7/6x+1)=0


Domain of the equation: x!=0

x∈R



Domain of the equation: 6x+1)!=0

x∈R


We get rid of parentheses

5/x-7/6x-1=0

We calculate fractions


30x/6x^2+(-7x)/6x^2-1=0

We multiply all the terms by the denominator


30x+(-7x)-1*6x^2=0

Wy multiply elements

-6x^2+30x+(-7x)=0

We get rid of parentheses

-6x^2+30x-7x=0

We add all the numbers together, and all the variables

-6x^2+23x=0

a = -6; b = 23; c = 0;
Δ = b2-4ac
Δ = 232-4·(-6)·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-23}{2*-6}=\frac{-46}{-12}
=3+5/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+23}{2*-6}=\frac{0}{-12}
=0
$