7/x-6=5x

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

7/x-6=5x

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-5x+7/x-6=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

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

a = -5; b = -6; c = +7;
Δ = b2-4ac
Δ = -62-4·(-5)·7
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*-5}=\frac{6-4\sqrt{11}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+4\sqrt{11}}{2*-5}=\frac{6+4\sqrt{11}}{-10}
$