5/x-6=7x

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

5/x-6=7x

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-7x+5/x-6=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

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

a = -7; b = -6; c = +5;
Δ = b2-4ac
Δ = -62-4·(-7)·5
Δ = 176
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{176}=\sqrt{16*11}=\sqrt{16}*\sqrt{11}=4\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-4\sqrt{11}}{2*-7}=\frac{6-4\sqrt{11}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+4\sqrt{11}}{2*-7}=\frac{6+4\sqrt{11}}{-14}
$