X+21/2x+10x=31

Solution for X+21/2x+10x=31 equation:

X+21/2X+10X=31

We move all terms to the left:

X+21/2X+10X-(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

11X+21/2X-31=0

We multiply all the terms by the denominator


11X*2X-31*2X+21=0

Wy multiply elements

22X^2-62X+21=0

a = 22; b = -62; c = +21;
Δ = b2-4ac
Δ = -622-4·22·21
Δ = 1996
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:

$\sqrt{\Delta}=\sqrt{1996}=\sqrt{4*499}=\sqrt{4}*\sqrt{499}=2\sqrt{499}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-62)-2\sqrt{499}}{2*22}=\frac{62-2\sqrt{499}}{44}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-62)+2\sqrt{499}}{2*22}=\frac{62+2\sqrt{499}}{44}
$