7x-41=6/x

Solution for 7x-41=6/x equation:

7x-41=6/x

We move all terms to the left:

7x-41-(6/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

7x-(+6/x)-41=0

We get rid of parentheses

7x-6/x-41=0

We multiply all the terms by the denominator


7x*x-41*x-6=0

We add all the numbers together, and all the variables

-41x+7x*x-6=0

Wy multiply elements

7x^2-41x-6=0

a = 7; b = -41; c = -6;
Δ = b2-4ac
Δ = -412-4·7·(-6)
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-41)-43}{2*7}=\frac{-2}{14}
=-1/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-41)+43}{2*7}=\frac{84}{14}
=6
$