2x+1/2x=1500

Solution for 2x+1/2x=1500 equation:

2x+1/2x=1500

We move all terms to the left:

2x+1/2x-(1500)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


2x*2x-1500*2x+1=0

Wy multiply elements

4x^2-3000x+1=0

a = 4; b = -3000; c = +1;
Δ = b2-4ac
Δ = -30002-4·4·1
Δ = 8999984
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:

$\sqrt{\Delta}=\sqrt{8999984}=\sqrt{16*562499}=\sqrt{16}*\sqrt{562499}=4\sqrt{562499}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3000)-4\sqrt{562499}}{2*4}=\frac{3000-4\sqrt{562499}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3000)+4\sqrt{562499}}{2*4}=\frac{3000+4\sqrt{562499}}{8}
$