x+2x+1/2x=59.50

Solution for x+2x+1/2x=59.50 equation:

x+2x+1/2x=59.50

We move all terms to the left:

x+2x+1/2x-(59.50)=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+2x+1/2x-(59.5)=0

We add all the numbers together, and all the variables

3x+1/2x-59.5=0

We multiply all the terms by the denominator


3x*2x-(59.5)*2x+1=0

We multiply parentheses

3x*2x-119x+1=0

Wy multiply elements

6x^2-119x+1=0

a = 6; b = -119; c = +1;
Δ = b2-4ac
Δ = -1192-4·6·1
Δ = 14137
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{-(-119)-\sqrt{14137}}{2*6}=\frac{119-\sqrt{14137}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-119)+\sqrt{14137}}{2*6}=\frac{119+\sqrt{14137}}{12}
$