1/2x=x+24

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

1/2x=x+24

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

1/2x-x-24=0

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 = 2312
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:

$\sqrt{\Delta}=\sqrt{2312}=\sqrt{1156*2}=\sqrt{1156}*\sqrt{2}=34\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-34\sqrt{2}}{2*-2}=\frac{48-34\sqrt{2}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+34\sqrt{2}}{2*-2}=\frac{48+34\sqrt{2}}{-4}
$