342/x-x=1

Solution for 342/x-x=1 equation:

342/x-x=1

We move all terms to the left:

342/x-x-(1)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-1x+342/x-1=0

We multiply all the terms by the denominator


-1x*x-1*x+342=0

We add all the numbers together, and all the variables

-1x-1x*x+342=0

Wy multiply elements

-1x^2-1x+342=0

a = -1; b = -1; c = +342;
Δ = b2-4ac
Δ = -12-4·(-1)·342
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-37}{2*-1}=\frac{-36}{-2}
=+18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+37}{2*-1}=\frac{38}{-2}
=-19
$