2x+1/2x=7.5

Solution for 2x+1/2x=7.5 equation:

2x+1/2x=7.5

We move all terms to the left:

2x+1/2x-(7.5)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

2x+1/2x-7.5=0

We multiply all the terms by the denominator


2x*2x-(7.5)*2x+1=0

We multiply parentheses

2x*2x-15x+1=0

Wy multiply elements

4x^2-15x+1=0

a = 4; b = -15; c = +1;
Δ = b2-4ac
Δ = -152-4·4·1
Δ = 209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-\sqrt{209}}{2*4}=\frac{15-\sqrt{209}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{209}}{2*4}=\frac{15+\sqrt{209}}{8}
$