1=2x+2/x+7

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

1=2x+2/x+7

We move all terms to the left:

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


Domain of the equation: x+7)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

-6x-2x*x-2=0

Wy multiply elements

-2x^2-6x-2=0

a = -2; b = -6; c = -2;
Δ = b2-4ac
Δ = -62-4·(-2)·(-2)
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{-(-6)-2\sqrt{5}}{2*-2}=\frac{6-2\sqrt{5}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{5}}{2*-2}=\frac{6+2\sqrt{5}}{-4}
$