1+x=7/x-2

Solution for 1+x=7/x-2 equation:

1+x=7/x-2

We move all terms to the left:

1+x-(7/x-2)=0


Domain of the equation: x-2)!=0

x∈R


We get rid of parentheses

x-7/x+2+1=0

We multiply all the terms by the denominator


x*x+2*x+1*x-7=0

We add all the numbers together, and all the variables

3x+x*x-7=0

Wy multiply elements

x^2+3x-7=0

a = 1; b = 3; c = -7;
Δ = b2-4ac
Δ = 32-4·1·(-7)
Δ = 37
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{-(3)-\sqrt{37}}{2*1}=\frac{-3-\sqrt{37}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{37}}{2*1}=\frac{-3+\sqrt{37}}{2}
$