.5x+1/3x=5

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Solution for .5x+1/3x=5 equation: 



.5x+1/3x=5

We move all terms to the left:

.5x+1/3x-(5)=0



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



We multiply all the terms by the denominator


(.5x)*3x-5*3x+1=0

We add all the numbers together, and all the variables

(+.5x)*3x-5*3x+1=0

We multiply parentheses

3x^2-5*3x+1=0

Wy multiply elements

3x^2-15x+1=0

a = 3; b = -15; c = +1;
Δ = b2-4ac
Δ = -152-4·3·1
Δ = 213
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{213}}{2*3}=\frac{15-\sqrt{213}}{6}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{213}}{2*3}=\frac{15+\sqrt{213}}{6}
$

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