x-1/x+5x/x-1+6=0

Solution for x-1/x+5x/x-1+6=0 equation:

x-1/x+5x/x-1+6=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

x-1/x+5x/x+5=0

We multiply all the terms by the denominator


x*x+5x+5*x-1=0

We add all the numbers together, and all the variables

10x+x*x-1=0

Wy multiply elements

x^2+10x-1=0

a = 1; b = 10; c = -1;
Δ = b2-4ac
Δ = 102-4·1·(-1)
Δ = 104
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:

$\sqrt{\Delta}=\sqrt{104}=\sqrt{4*26}=\sqrt{4}*\sqrt{26}=2\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{26}}{2*1}=\frac{-10-2\sqrt{26}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{26}}{2*1}=\frac{-10+2\sqrt{26}}{2}
$