7x-4/x=1

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

7x-4/x=1

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

7x^2-1x-4=0

a = 7; b = -1; c = -4;
Δ = b2-4ac
Δ = -12-4·7·(-4)
Δ = 113
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{-(-1)-\sqrt{113}}{2*7}=\frac{1-\sqrt{113}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{113}}{2*7}=\frac{1+\sqrt{113}}{14}
$