x-1/2x=48

Solution for x-1/2x=48 equation:

x-1/2x=48

We move all terms to the left:

x-1/2x-(48)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


x*2x-48*2x-1=0

Wy multiply elements

2x^2-96x-1=0

a = 2; b = -96; c = -1;
Δ = b2-4ac
Δ = -962-4·2·(-1)
Δ = 9224
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:

$\sqrt{\Delta}=\sqrt{9224}=\sqrt{4*2306}=\sqrt{4}*\sqrt{2306}=2\sqrt{2306}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-2\sqrt{2306}}{2*2}=\frac{96-2\sqrt{2306}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+2\sqrt{2306}}{2*2}=\frac{96+2\sqrt{2306}}{4}
$