10=7x+1/x-2

Solution for 10=7x+1/x-2 equation:

10=7x+1/x-2

We move all terms to the left:

10-(7x+1/x-2)=0


Domain of the equation: x-2)!=0

x∈R


We get rid of parentheses

-7x-1/x+2+10=0

We multiply all the terms by the denominator


-7x*x+2*x+10*x-1=0

We add all the numbers together, and all the variables

12x-7x*x-1=0

Wy multiply elements

-7x^2+12x-1=0

a = -7; b = 12; c = -1;
Δ = b2-4ac
Δ = 122-4·(-7)·(-1)
Δ = 116
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:

$\sqrt{\Delta}=\sqrt{116}=\sqrt{4*29}=\sqrt{4}*\sqrt{29}=2\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{29}}{2*-7}=\frac{-12-2\sqrt{29}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{29}}{2*-7}=\frac{-12+2\sqrt{29}}{-14}
$