6/x-7=5x

Solution for 6/x-7=5x equation:

6/x-7=5x

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-5x+6/x-7=0

We multiply all the terms by the denominator


-5x*x-7*x+6=0

We add all the numbers together, and all the variables

-7x-5x*x+6=0

Wy multiply elements

-5x^2-7x+6=0

a = -5; b = -7; c = +6;
Δ = b2-4ac
Δ = -72-4·(-5)·6
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-13}{2*-5}=\frac{-6}{-10}
=3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+13}{2*-5}=\frac{20}{-10}
=-2
$