X+1/2x=24

Solution for X+1/2x=24 equation:

X+1/2X=24

We move all terms to the left:

X+1/2X-(24)=0


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We multiply all the terms by the denominator


X*2X-24*2X+1=0

Wy multiply elements

2X^2-48X+1=0

a = 2; b = -48; c = +1;
Δ = b2-4ac
Δ = -482-4·2·1
Δ = 2296
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:

$\sqrt{\Delta}=\sqrt{2296}=\sqrt{4*574}=\sqrt{4}*\sqrt{574}=2\sqrt{574}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-2\sqrt{574}}{2*2}=\frac{48-2\sqrt{574}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+2\sqrt{574}}{2*2}=\frac{48+2\sqrt{574}}{4}
$