x-1/x+7=3

Solution for x-1/x+7=3 equation:

x-1/x+7=3

We move all terms to the left:

x-1/x+7-(3)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x-1/x+4=0

We multiply all the terms by the denominator


x*x+4*x-1=0

We add all the numbers together, and all the variables

4x+x*x-1=0

Wy multiply elements

x^2+4x-1=0

a = 1; b = 4; c = -1;
Δ = b2-4ac
Δ = 42-4·1·(-1)
Δ = 20
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:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{5}}{2*1}=\frac{-4-2\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{5}}{2*1}=\frac{-4+2\sqrt{5}}{2}
$