7x-4-7/x=0

Solution for 7x-4-7/x=0 equation:

7x-4-7/x=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

7x^2-4x-7=0

a = 7; b = -4; c = -7;
Δ = b2-4ac
Δ = -42-4·7·(-7)
Δ = 212
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:

$\sqrt{\Delta}=\sqrt{212}=\sqrt{4*53}=\sqrt{4}*\sqrt{53}=2\sqrt{53}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{53}}{2*7}=\frac{4-2\sqrt{53}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{53}}{2*7}=\frac{4+2\sqrt{53}}{14}
$