x+1/2x=25.80

Solution for x+1/2x=25.80 equation:

x+1/2x=25.80

We move all terms to the left:

x+1/2x-(25.80)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

x+1/2x-(25.8)=0

We add all the numbers together, and all the variables

x+1/2x-25.8=0

We multiply all the terms by the denominator


x*2x-(25.8)*2x+1=0

We multiply parentheses

x*2x-51.6x+1=0

Wy multiply elements

2x^2-51.6x+1=0

a = 2; b = -51.6; c = +1;
Δ = b2-4ac
Δ = -51.62-4·2·1
Δ = 2654.56
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{-(-51.6)-\sqrt{2654.56}}{2*2}=\frac{51.6-\sqrt{2654.56}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51.6)+\sqrt{2654.56}}{2*2}=\frac{51.6+\sqrt{2654.56}}{4}
$