7/x=x+2-7+8

Solution for 7/x=x+2-7+8 equation:

7/x=x+2-7+8

We move all terms to the left:

7/x-(x+2-7+8)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

7/x-(x+3)=0

We get rid of parentheses

7/x-x-3=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

-3x-x*x+7=0

Wy multiply elements

-1x^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}
$