x+5/2x+10=31

Solution for x+5/2x+10=31 equation:

x+5/2x+10=31

We move all terms to the left:

x+5/2x+10-(31)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

x+5/2x-21=0

We multiply all the terms by the denominator


x*2x-21*2x+5=0

Wy multiply elements

2x^2-42x+5=0

a = 2; b = -42; c = +5;
Δ = b2-4ac
Δ = -422-4·2·5
Δ = 1724
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:

$\sqrt{\Delta}=\sqrt{1724}=\sqrt{4*431}=\sqrt{4}*\sqrt{431}=2\sqrt{431}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{431}}{2*2}=\frac{42-2\sqrt{431}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{431}}{2*2}=\frac{42+2\sqrt{431}}{4}
$