7/x-5=6x

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

7/x-5=6x

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-6x+7/x-5=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

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

a = -6; b = -5; c = +7;
Δ = b2-4ac
Δ = -52-4·(-6)·7
Δ = 193
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{193}}{2*-6}=\frac{5-\sqrt{193}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{193}}{2*-6}=\frac{5+\sqrt{193}}{-12}
$