7x-1/x=4

Solution for 7x-1/x=4 equation:

7x-1/x=4

We move all terms to the left:

7x-1/x-(4)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


7x*x-4*x-1=0

We add all the numbers together, and all the variables

-4x+7x*x-1=0

Wy multiply elements

7x^2-4x-1=0

a = 7; b = -4; c = -1;
Δ = b2-4ac
Δ = -42-4·7·(-1)
Δ = 44
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:

$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{11}}{2*7}=\frac{4-2\sqrt{11}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{11}}{2*7}=\frac{4+2\sqrt{11}}{14}
$