4x+1/2x=24

Solution for 4x+1/2x=24 equation:

4x+1/2x=24

We move all terms to the left:

4x+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


4x*2x-24*2x+1=0

Wy multiply elements

8x^2-48x+1=0

a = 8; b = -48; c = +1;
Δ = b2-4ac
Δ = -482-4·8·1
Δ = 2272
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:

$\sqrt{\Delta}=\sqrt{2272}=\sqrt{16*142}=\sqrt{16}*\sqrt{142}=4\sqrt{142}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-4\sqrt{142}}{2*8}=\frac{48-4\sqrt{142}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+4\sqrt{142}}{2*8}=\frac{48+4\sqrt{142}}{16}
$