2x+71/x=142

Solution for 2x+71/x=142 equation:

2x+71/x=142

We move all terms to the left:

2x+71/x-(142)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


2x*x-142*x+71=0

We add all the numbers together, and all the variables

-142x+2x*x+71=0

Wy multiply elements

2x^2-142x+71=0

a = 2; b = -142; c = +71;
Δ = b2-4ac
Δ = -1422-4·2·71
Δ = 19596
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:

$\sqrt{\Delta}=\sqrt{19596}=\sqrt{4*4899}=\sqrt{4}*\sqrt{4899}=2\sqrt{4899}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-142)-2\sqrt{4899}}{2*2}=\frac{142-2\sqrt{4899}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-142)+2\sqrt{4899}}{2*2}=\frac{142+2\sqrt{4899}}{4}
$