6/x-5=4x

Solution for 6/x-5=4x equation:

6/x-5=4x

We move all terms to the left:

6/x-5-(4x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-4x+6/x-5=0

We multiply all the terms by the denominator


-4x*x-5*x+6=0

We add all the numbers together, and all the variables

-5x-4x*x+6=0

Wy multiply elements

-4x^2-5x+6=0

a = -4; b = -5; c = +6;
Δ = b2-4ac
Δ = -52-4·(-4)·6
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-11}{2*-4}=\frac{-6}{-8}
=3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+11}{2*-4}=\frac{16}{-8}
=-2
$