0,5x+1/3x+0,25x=13

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Solution for 0,5x+1/3x+0,25x=13 equation: 



0.5x+1/3x+0.25x=13

We move all terms to the left:

0.5x+1/3x+0.25x-(13)=0



Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



We add all the numbers together, and all the variables

0.75x+1/3x-13=0

We multiply all the terms by the denominator


(0.75x)*3x-13*3x+1=0

We add all the numbers together, and all the variables

(+0.75x)*3x-13*3x+1=0

We multiply parentheses

0x^2-13*3x+1=0

Wy multiply elements

0x^2-39x+1=0

We add all the numbers together, and all the variables

x^2-39x+1=0

a = 1; b = -39; c = +1;
Δ = b2-4ac
Δ = -392-4·1·1
Δ = 1517
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{-(-39)-\sqrt{1517}}{2*1}=\frac{39-\sqrt{1517}}{2}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+\sqrt{1517}}{2*1}=\frac{39+\sqrt{1517}}{2}
$

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