(7/x)+3=x-1

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

(7/x)+3=x-1

We move all terms to the left:

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


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

7/x-x+1+3=0

We multiply all the terms by the denominator


-x*x+1*x+3*x+7=0

We add all the numbers together, and all the variables

4x-x*x+7=0

Wy multiply elements

-1x^2+4x+7=0

a = -1; b = 4; c = +7;
Δ = b2-4ac
Δ = 42-4·(-1)·7
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*-1}=\frac{-4-2\sqrt{11}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{11}}{2*-1}=\frac{-4+2\sqrt{11}}{-2}
$