4/x+1=x+7

Solution for 4/x+1=x+7 equation:

4/x+1=x+7

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We get rid of parentheses

4/x-x-7+1=0

We multiply all the terms by the denominator


-x*x-7*x+1*x+4=0

We add all the numbers together, and all the variables

-6x-x*x+4=0

Wy multiply elements

-1x^2-6x+4=0

a = -1; b = -6; c = +4;
Δ = b2-4ac
Δ = -62-4·(-1)·4
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{13}}{2*-1}=\frac{6-2\sqrt{13}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{13}}{2*-1}=\frac{6+2\sqrt{13}}{-2}
$