6x-7=4/x

Solution for 6x-7=4/x equation:

6x-7=4/x

We move all terms to the left:

6x-7-(4/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

6x-(+4/x)-7=0

We get rid of parentheses

6x-4/x-7=0

We multiply all the terms by the denominator


6x*x-7*x-4=0

We add all the numbers together, and all the variables

-7x+6x*x-4=0

Wy multiply elements

6x^2-7x-4=0

a = 6; b = -7; c = -4;
Δ = b2-4ac
Δ = -72-4·6·(-4)
Δ = 145
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{-(-7)-\sqrt{145}}{2*6}=\frac{7-\sqrt{145}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{145}}{2*6}=\frac{7+\sqrt{145}}{12}
$