2.x-1=16/x.7+1

Solution for 2.x-1=16/x.7+1 equation:

2.x-1=16/x.7+1

We move all terms to the left:

2.x-1-(16/x.7+1)=0


Domain of the equation: x.7+1)!=0

x∈R


We get rid of parentheses

2.x-16/x.7-1-1=0

We multiply all the terms by the denominator


(2.x)*x.7-1*x.7-1*x.7-16=0

We add all the numbers together, and all the variables

(+2.x)*x.7-1*x.7-1*x.7-16=0

We multiply parentheses

2x^2-1*x.7-1*x.7-16=0

Wy multiply elements

2x^2-1x-1x-16=0

We add all the numbers together, and all the variables

2x^2-2x-16=0

a = 2; b = -2; c = -16;
Δ = b2-4ac
Δ = -22-4·2·(-16)
Δ = 132
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:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{33}}{2*2}=\frac{2-2\sqrt{33}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{33}}{2*2}=\frac{2+2\sqrt{33}}{4}
$