X+1/2x=36

Solution for X+1/2x=36 equation:

X+1/2X=36

We move all terms to the left:

X+1/2X-(36)=0


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We multiply all the terms by the denominator


X*2X-36*2X+1=0

Wy multiply elements

2X^2-72X+1=0

a = 2; b = -72; c = +1;
Δ = b2-4ac
Δ = -722-4·2·1
Δ = 5176
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:

$\sqrt{\Delta}=\sqrt{5176}=\sqrt{4*1294}=\sqrt{4}*\sqrt{1294}=2\sqrt{1294}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-2\sqrt{1294}}{2*2}=\frac{72-2\sqrt{1294}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+2\sqrt{1294}}{2*2}=\frac{72+2\sqrt{1294}}{4}
$