31/x+x-7+x+126=180

Solution for 31/x+x-7+x+126=180 equation:

31/x+x-7+x+126=180

We move all terms to the left:

31/x+x-7+x+126-(180)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

2x+31/x-61=0

We multiply all the terms by the denominator


2x*x-61*x+31=0

We add all the numbers together, and all the variables

-61x+2x*x+31=0

Wy multiply elements

2x^2-61x+31=0

a = 2; b = -61; c = +31;
Δ = b2-4ac
Δ = -612-4·2·31
Δ = 3473
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-61)-\sqrt{3473}}{2*2}=\frac{61-\sqrt{3473}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-61)+\sqrt{3473}}{2*2}=\frac{61+\sqrt{3473}}{4}
$