X+1/2x=20

Solution for X+1/2x=20 equation:

X+1/2X=20

We move all terms to the left:

X+1/2X-(20)=0


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We multiply all the terms by the denominator


X*2X-20*2X+1=0

Wy multiply elements

2X^2-40X+1=0

a = 2; b = -40; c = +1;
Δ = b2-4ac
Δ = -402-4·2·1
Δ = 1592
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:

$\sqrt{\Delta}=\sqrt{1592}=\sqrt{4*398}=\sqrt{4}*\sqrt{398}=2\sqrt{398}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-2\sqrt{398}}{2*2}=\frac{40-2\sqrt{398}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+2\sqrt{398}}{2*2}=\frac{40+2\sqrt{398}}{4}
$